I like what Xuvie said first about short sentences.
Think of it like a movie scene, and however long your sentence or your description is, is how long looking at that thing, or doing that action is taking.

For example: "She swung her leg out, tripping him." sounds really quick, while "she spun her leg in a wide circle, tripping her opponent" makes it seem like one of those scenes in sherlock holmes where he thinks a few moves ahead, and time slows down for the reader/viewer.

The other trick is to limit your narration, or the internal monologue of your POV character. Assume that the only thing that is on their mind is exactly what is going on then and there. It brings a sense of urgency. If the only thing your character is worrying about is punching that other person, or not getting punched, then the reader knows that things are kind of dire.

Your action scenes don't have to be short to not drag on, they just have to have a sense of urgency.