[Simple]

I was looking at the amateur to intermediate requirements and saw that my fighting tut was there, but it wasn't done yet and most of the links were broke, and thought, "Hey, why don't I make another tut?" so here I go.

First, pick a base stick to use and create a line for the ground. You CAN use more than one type of stick, and I used to all the time, but it is easier and often looks better with only one.

DO NOT USE THE DEFAULT STICK!

It is a bad stick, especially for beginners, who will learn how to do things wrong using the default stick. Sometimes pros like to mess around with it, but they can, because they actually know how to use it well.
Example of Bad Default Use
See what's wrong with it? The defaults are stick thin and weirdly proportioned so that normal actions look awkward. They also have no backbone, so it is hard to make realistic reactions.

Here is the base stick I will be using for this tutorial:
Longlegs
If you borrow someone else's sticks for your animation, keep track of which ones they are and who they belong to, so that you can give credit. It's common courtesy.

If your base stick is a different color from the floor, then make sure it is in front. Also, be careful not to let your stick's feet go under the floor.
Bad:

Good:


See why it's important?

Okay. This step is optional, but it is good to do once you have developed your skills enough. A lot of times people just animate random fights for no apparent reason. It's not BAD really, but sometimes it's fun to see how it got started.
For example:

It just seems to come out of nowhere doesn't it?

With this anim, there is motive and story to it. The weird green mutant thing is taken captive by Darkdemon, so he has to fight his way out. If I had left out the first scene, it wouldn't have made any sense at all.
The animation is equally good, the second just makes a little more sense.

Lets start with the basics: punching and kicking.

PUNCHING
Punching is the most basic method of combat, so it is important you know how to animate it.
Bad punching
Okay, first off, this uses the DEFAULT, so lets change it to my stick.
With Better Stick
It almost looks worse now though, doesn't it? Such a big guy looks dorky and stupid when he's stiff like that. Let's loosen him up a bit.
Better Motion
See what I did? I moved his other arm backward as he punched to create more natural-looking motion. It's still not good though. He's still freakishly stiff. We'll fix this by making other parts of his body move.
More Motion
That's a lot better! He steps forward as he punches, making it seem like a real punch, and he adjusts by shifting his weight around. Now all we need to do is add "easing".
See how the guy is moving at a constant rate, with no variance at all? It looks unnatural and confusing, so we have easing. Easing is where the character gradually slows down and speeds up as it moves. I'm not going to go into detail on this concept, there are easing tuts out there.
So I add easing, and...

.piv
That's pretty much it with punching. I know there is another style of punch where the you do the same thing up until frame 8 or 9, but then you fold the arm in half and stick it out in front, and then unfold it the next frame, but I don't like it. It's choppy and (I think) it's lazy. Learn real punches.

Kicking
Throw in all the punches you want, it gets boring after a while. You need to toss in a few kicks. Kicking works almost the same as punching, it's just a little harder to get the right motion.
Bad Kicking
Default alert!
With Better Stick
But now he's stiff.
Better Motion
Doesn't really help much. Everything needs to be moving.
More Motion
Now this is where it gets tricky, and even if you try to work this out when you are first animating each frame, you will almot always end up having to adjust it a little. At least this is true for me. Placement. Placement of each limb is crucial, and if something is out of place, it can throw off the whole anim. This is especially true with kicks, where everything has to be timed just right. I'll add easing too, just so I don't have to readjust for when I ease everything.
The finished product...

.piv
Okay. I admit it's not the greatest kick, but you get the idea.
Here's a better kick: http://img103.imageshack.us/img103/2...mbofailrm1.gif
Not the same style of kick though, but whatever.

A few tips:
1. Don't make your actions so smooth that they look weak. Balance speed variation/power with fluency/easing.
2. Make sure your character's physics are believable. No normal person can do a powerful high-kick, hold it there for three seconds, and then land normally. Sometimes you don't have to have perfect realism, but it's a good skill.
3. Animate normally. Don't do it in steps like this tutorial. I just used that method to show you the difference between good and bad. BUT-Don't be afraid to fix things if you don't like how they look. Everyone makes mistakes.
4. Focus on detail. If a kick or punch looks good, but the stick is flopping all over the place, it's just like it was a bad punch or kick.

I think that's it on the basics...
[TBC]