There are three different principles to follow when creating action scenes, I don’t always follow them perfectly myself, but when I do the results are generally better then normal.
A note, motion blurs, speed lines and other tricks are fine and add a lot to a scene. But it's always good to practice having a lively scene without these, there is always the danger that one begins to use them as a crutch. Even without these, your art should appear to be in movement. Blurs and so on are just icing on the cake.
1. Pose,
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Try to find a pose which conveys motion. As I said before, the more stable the pose of a figure, the more weight it has directly on the ground, the more static it will appear to the viewer. Choose a pose where the figure bends and twists, show a person leaning into a punch, show a horse or pony rearing on its hind legs, mid gallop or so on.
Don’t be afraid to show unfinished actions. If a viewer sees a figure in the middle of an action, they can easily imagine it in motion and it will leave them wondering and imagining how the action scene will end. Always a good thing.
If you are doing more unrealistic illustrations, cartoons, comics, mangas, or what have you, don’t be afraid to exaggerate the pose. Or even more realistic works. The American Western artist Frederic Remington (an inspiration of mine when drawing horses) often drew using photographic references and he was one of the first painters to properly show a horse with a realistic gallop. However, he admitted to exaggerating the actions of his subjects to show motion, he didn't let reality get in the way of a good picture! Of course, there is fine line between artful exaggeration and a odd mess.
2. Reaction,
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When drawing, the force of the illustrated action can be easily measured by its reaction. I'm not strictly referring to the Newtonian reaction, but the person or thing reacting the action. For example, a man being punched is reacting to the punch. There probably is better language for this, but I have no formal art training.
If you draw someone punching, the viewer will gauge the force of the punch by the reaction of the person being punched. Thus you can create some ridiculous comic style scenes by creating insane reactions. For example, you can draw a picture of a person flicking someone else, causing them to fly through a wall. And it would look fine, if ludicrous. The reactions of an action don't just include people, but also dust clouds, debris, or anything else. If you include proper reactions in your action scene, it will come to life very easily.
A long time ago I brought a how to draw book written by several comic book authors, most of it was obscure and gave little practical advice. However, one of the writers actually gave some very good tips on action and reaction. The central one was to draw the reaction first, then the action. Now this may seem counter intuitive as the reaction follows the action, but (at least for me) it really works. During the pre-drawing stage, draw the person being punched or kicked first and then draw the person doing the kicking, I’m really not sure why this works out better and looks more natural. I guess because the action must match the reaction it is easier to work backwards. I don't know, it is something to try at the very least.
3. Dynamic Camera Angle,
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The final one is camera angle. Certain action scenes look better from certain points of view. Now, in my personal opinion, front and three-quarters view are the easiest to portray dynamic action scenes. There is something about action that is coming toward you or away which makes it more personal, and thus interesting. You can also place the action in the background and the reaction in the foreground as well. Then the viewer has more empathy with the person reacting.
The profile view is the hardest, or when the action is moving strictly left from right or vice-versa. Because then the viewer is more a spectator viewing the action and thus the action seems to have less of an effect on them. However, the view is useful at times, though hard to get right. I find it is useful in battle scenes were you want to portray opposite forces and give equal picture weight to both.
However, there is a second reason why the front and three quarters views are better at conveying action and that is because it is easy to set up a vanishing point. Nothing adds to an action scene then foreshortening and a vanishing point. Properly done, the action will leap off the page, improperly and it’ll look like a jumbled mess. However, even a simple one vanishing point scene can be pretty tricky, as it is; I rarely do it on account of time and laziness.