Fighting techniques of the axe, halberd, and poleaxe
1. The Axe
This category includes both utility axes pressed into a combat role and dedicated battleaxes that lack any such projections such as a top spike, a fluke/beak, or a buttspike. As you can expect, all these axes look essentially the same as utility axes, but looks can be deceiving; within this group there's a substantial variance in weight, balance, and mass distribution. The simplest aspect of this variability is that axes designed specifically for combat tend to be lighter than utility axes, for reasons I've explained in the other post.
The most practical first step in learning the use of such simple battleaxes--whether the one- or two-handed variety--is to visit the nearest lumberjack's house or Boy Scout camp. Seriously. The body mechanics involved in swinging a battleaxe is fundamentally the same as that for using a utility axe. There is no better example of this than the use of the two-handed battleaxe. A right-handed man would usually hold a two-handed felling axe with his left hand near the end of the haft and the right hand almost next to the head (the axe's, that is, not the man's). As he swings, his right hand would slide down the haft until it's right next to the left hand by the time the axe hits the tree. This sliding motion allows the delivery of a powerful chopping blow with the least waste of energy. The same principle applies to the two-handed battleaxe; an experienced reenactor (R. Montague Smith, if I'm not mistaken) once told me that "you split a shield the same way you split a log."
Another lesson that a battle-axe fighter can learn from utility axes is that there is more than one way to use an axe. To use the two-handed axe example once again, the sliding-hand blow is fine against a fairly distant targets, but for hacking at closer targets (read : enemies) you can slide the hand a bit less or even not slide it at all. What if the enemy is right in front of your nose? Of course, you can't hit the poor bastard with your axe-head in that position, but remember that you can whack him on the head with the end of your axe's haft. Other than that, the top of an axe-head may have an upcurving profile that provides you with a thrusting point; even in the absence of such a point, the axe-head itself usually has enough mass to deliver a blunt thrusting blow with enough force to seriously harass your enemy. (Some people find this a little hard to believe until they get poked in the pit of the stomach by a blunt thrust with an axe-head.)
Hooking is a very useful but also very commonly misunderstood mode of attack with the axe. Untrained people would be prone to "hook" by doing just that--swinging the axe in a curved motion to get around and hook the target in a single movement. This is not the right way to do it, however, since the movement relies too much on the axe-wielders' arms rather than using the whole body to pull the enemy in. It also makes the axe-wielder's intent obvious and may allow the enemy a chance to easily dodge or counter the attack. How are we supposed to do it, then? The most effective way is to swing the axe as usual, aiming at a point behind the enemy; and then, when the haft strikes the enemy's body, the wielder should fix the axe in that position relative to his/her own body and then shift the whole body back by sliding the rear foot backwards. This movement will also lower the axe-wielder's center of gravity, which is quite a desirable side effect because it stabilizes the axe-wielder against the hooked enemy. Additionally, the "strike-and-pull" approach highlights the important fact that the hooking movement is basically the axe's equivalent of a close-range slice with the sword. (In other words, the Three Wounders for a sword is the Cut, Thrust, and Slice, while for an axe it's the Hack, Poke, and Hook.) This strike-and-pull hooking movement is best performed against the knee, the hands, or the neck; but it can also do considerable damage against the torso, and of course it can also hook the opponent's weapon, especially if that weapon has a projection (such as an axehead or a beak) for the hooking axe-head to catch on to.
So far I've mostly talked about two-handed battleaxes. What about the one-handed variant? The same basic ideas apply--you can thrust with the head, smack the enemy down with the end of the haft, or hook him with the strike-and-pull movement just like you would with a two-handed axe. The principal difference, perhaps, is the idea of sliding the grip; with a one-handed axe, you obviously don't slide your hand while delivering a full-powered blow at the optimum range, and when you need to swing at enemies closer than this you'd just move your grip altogether up the haft rather than changing the amount of sliding done by the farther hand.
As in swordfighting, real axe-fighting doesn't employ blocks anywhere near as much as Hollywood does. The axe's haft is generally more fragile than a sword's blade, so it's not as good at deflecting the enemy's blows either. This leaves voiding (dodging) and distance control as an axe-wielder's primary means of defense, preferably combined with adequate armor or a sufficiently large shield. It's no surprise to me that Anglo-Saxon housecarles who wielded the two-handed Dane axe at the Battle of Hastings (1066) were mostly armored in knee-length hauberks of mail and conical helmets--the heaviest kind of armor in general use in their time and region.
(The Hurstwic reenactment group has an excellent article about axes and axe-fighting in the Viking period; the article's narrower chronological and geographical focus allows it to go into greater detail on some points than this post, and I'd strongly recommend the curious reader to check it out.)
2. The Halberd
Why just the halberd? Why not other kinds of polearms, like the bill, the voulge, the glaive, or what-have-you?
Because such a detailed classification of polearms by visual features may be useful to a museum curator, but it's largely meaningless to a martial artist. As long as it has a long stave (6 feet or longer) with a broad cutting head and a spike, spearhead, or thrusting point on top, its method of use would be quite similar to the halberd and a European martial artist wouldn't see the need to build an entirely new style of polearm use around it.
In its most highly-developed form, the halberd (and similar weapons) has five different appliances for hurting the enemy: a point/spike/spearhead on top, a cleaving blade/bill/axehead, a hooked beak at the back, the butt of the staff (often covered with a buttspike), and the staff itself. So it's effectively a two-handed spear, an axe, and a staff lumped together into a deadly package. The most common beginners' mistake in using the halberd is putting too much emphasis on only one or two means of striking while almost entirely neglecting the rest.
One good way to hold the halberd is to to start with one hand at or near the middle of the staff, thumb pointing towards the spearhead. The other hand should then be placed closer to the butt, far enough from the central hand that there's enough leverage for a powerful blow but close enough that there's still a fairly long section of the staff projecting below the hand. This last point is important because one of the most useful guards for the halberd is the high ward, where both hands are held above the head and the butt of the staff points forwards and downwards at the enemy's face. Untrained people might think that this guard is only good for delivering a massive downwards blow with the axehead; they're right about the power of the vertical blow, but wrong in that it's definitely not the only possible way to attack or defend with the high ward. In fact, one of the reasons why the high ward is so versatile is that the projecting butt section of the staff can be used both to thrust and to set aside the enemy's strikes. The defensive capability of the butt is particularly useful against an opponent armed with a spear or a similar thrusting polearm because it allows the halberdier to strike the incoming thrust aside and then follow up with a downwards strike of the axehead. Alternatively, the halberdier can whirl the halberd in one smooth circular movement to set the enemy's thrust aside with the butt, lever the enemy's shaft upwards so that it points harmlessly into the sky, and follow up to strike the enemy's head or shoulder with either the axehead or the beak. Of course, the blow is likely to come up short or long, but this is no problem for the halberdier; if it falls short, he can just turn the strike into a thrust against the enemy's face or upper body, while if it ends up long he can hook the enemy with a strike-and-pull movement quite similar to what an axeman would use in the same situation. It should be obvious by now that this hooking movement can be accomplished by both the the axehead and the beak.
This mention of hooking brings us to perhaps the most controversial part of the archetypal halberd: the beak. This projection, sticking out in the opposite direction from the cutting head, is often said to be a tool for piercing plate armor. I suspect the people who said this has never had the chance to actually test the beak against an armored man. First of all, the beak is so small and rests near the end of such a long staff that it's quite hard to employ it to hit plate armor at the square angle needed if it is to have any real chance at penetration. A blow landing at anything other than a square-on angle would just skid off harmlessly from the armor; after all, this is how the smooth deflecting surfaces of plate armor are meant to work. And then, even if the beak does penetrate the armor, this penetration is not likely to be deep enough to cause any serious injuries. Fortunately this doesn't mean that the beak is altogether useless. The other popular conception of its use--as a device for hooking--is entirely correct, as its inwardly curved shape attests. Why, then, did I say "strike with the beak" in the explanation about the possible attacks from the high ward? Because you'll have to try striking with it anyway as a preliminary to hooking in the strike-and-pull manner. This strike would most likely miss in the sense that the beak would probably not hit the enemy square-on, but such a miss is not undesirable because it would usually place the beak in a perfect position for the "pull" half of the hooking motion.
So far we've dealt with only the high ward--and it's only one ward among many. The next ward--let's call it the "window" ward--also has both hands above the head, but now it's the spearhead rather than the butt that points towards the enemy. After that comes the level ward, where the shaft is held level beside the body with the head pointing forwards at the opponent's navel. And then there's the middle ward, very similar to the level ward except that the rear hand is held a little lower so that the spearhead is pointing at the enemy's face. These three wards are fundamentally thrusting wards and the halberd operates from them much like a somewhat heavier version of the spear. With one exception, that is. Against an opponent with a sufficiently long weapon (especially a polearm), the halberdier can begin from the level or middle ward, slide his halberd under the opponent's, and then raise the halberd up with the opponent's weapon caught in the crook between spearhead and axehead or spearhead and beak. This movement, when done in conjunction with a passing step forward, will put the halberdier in a good position to strike a downwards blow. The enemy would be in no position to pre-empt the blow with the head of the polearm because the halberd, being in the lower position, would always arrive first. That doesn't mean the attack has no effective counter, though. Imagine that it was your opponent who had lifted your weapon in this way; you'd have a window of opportunity while the high position of his weapon leaves his body wide open, and you can take advantage of it by stepping forward to close the distance even further and thrusting the butt of your weapon into his thigh or stomach. Then you can finish him with a downwards blow from your own axe-head.
On a massed battlefield, the halberdier's choices would be somewhat more limited because there are many techniques he wouldn't be able to execute without running afoul of his friends. Basically he'd have the spearhead and the buttspike for use in the defensive role; both of them can also be employed offensively, along with a straight downward blow with the axehead. Now, while the halberd is often characterized as a weapon best used against heavily-armored horsemen, I think this idea of the halberd's use is somewhat incorrect. Of course, the halberd can work against horsemen; but the halberdiers' best bet in this instance is just to huddle together and present their spikes/spearheads out towards the horsemen, making them no different than any other spear-based formation. So no, there's nothing unique in the halberd's capability to face down a mounted adversary. If anything, the halberd most frequently saw use and was at its best when fighting against infantry formations with less than complete armor, such as the Swiss and the Landsknechts. The addition of small halberdier groups into pike formations seemed to have given the pikes more flexibility and striking power, especially in rough terrain where the pike blocks were prone to breaking up and didn't have enough space to deliver the full impact of an all-out pike charge.
The wards and techniques described above are mostly ripped straight out of di Grassi, with a few additions and modifications from other systems. I'm quite sure that they represent only a tiny fraction of the halberd-lore available in European martial arts; in particular, they don't include many of the sophisticated techniques from the German and Bolognese schools, mostly because I haven't found the time to study and experiment with them. Nevertheless, I hope they can give the lay audience (especially fiction writers) a small picture of what the halberd (and similar weapons) are capable of, as well as helping to dispel the myth that this hoplological family contains nothing more than a bunch of crude, unrefined weapons. Better still if the whole thing can motivate the reader to do further research on his/her own!
(Note: a book I'd particularly recommend for those who want to do a more detailed study into halberds and other polearm techniques is The Polearms of Paulus Hector Mair by David Knight and Brian Hunt.)
3. The Poleaxe
I'll be brief, trust me. I think the polearms menagerie does neither the halberd nor the poleaxe any justice by saying that the two are identical with each other. Yes, there's a great deal of overlap between the two. No, that doesn't make them the same. Most importantly, the halberd always has a cutting axehead, whereas the poleaxe--despite its name--often has no axehead at all.
Strange isn't it? The names for the poleaxe in other European languages--Hache, Azza, or Streitaxt--explicitly refer to the axe, but most of the texts that name the weapon in this way show it with a hammerhead and a beak, leaving no space for the axe. If we look at surviving historical examples, weapons that fall within the "poleaxe" category are best defined by the presence of the dague (top spike) and the queue (buttspike), while the heads may have an axehead or a mail (hammerhead) on the front and a mail or a beak at the back. Its most significant difference from the halberd is in terms of employment; halberd techniques are mostly designed for maximum utility against opponents with less than complete armor while poleaxe techniques focus on fighting against fully-armored opponents, especially those in full harnesses of plate. This is frequently made explicit in the text and illustrations of fighting manuals that deal with the poleaxe. Still, as with the material aspects, there's generally a significant overlap between halberd and poleaxe techniques.
As you can expect, the martial category of "poleaxe" covers weapons that a museum curator would split into several different visual categories--among which are the bec de corbin/bec de faucon and the Lucerne hammer. The usage of all these weapons would have been pretty much identical to a medieval or Renaissance warrior.
All right. So how do you use them? I wouldn't presume to claim any expertise in this respect, because I've never experimented with the techniques in any poleaxe manual yet--unlike the halberd, with which I've made at least a few awkward attempts. I can suggest several possible sources, though. One is the myArmoury article on the poleaxe, another is Professor Sydney Anglo's translation of the Jeu de la Hache, and finally there is Hugh Knight's Schlachtschule, a group that has done a lot of interpretative work on medieval and Renaissance poleaxe texts*. David Knight and Brian Hunt's book on Paulus Hector Mair's polearm techniques also includes a section on the poleaxe, so curious readers might want to check that one out too.
*P.S.: The Schlachtschule has recently put up a number of youTube videos, one of which shows several excellent examples of historical poleaxe techniques.