We do have a training tag, so there should be some useful ideas there.
The simplest way? Make the sequence educational. The point is to teach your characters something. This means you need to know something on the subject (and if you don’t, then it’s time to do some research). Then you impart that information to your audience. Teach them something they didn’t know.
This doesn’t change when it comes to martial arts or other kinds of combat training. The physical training will be coupled with an explanation for what to do and why. Depending on the instructor, the “why” could be occluded with mysticism, in an attempt to push the student (and reader) to think. But, it still needs to be there. I would strongly warn you against going for a pseudo-mystical explanation of “why,” unless you’re actually pretty well versed in the philosophy your character is working from.
Training sequences live and die on the lessons your characters teach. Strictly speaking, this can go both ways. There’s a cliche element to the teacher learning from the student, but it is something that happens.
Training sequences are also a very good time to slip in exposition dumps without getting caught. Your characters are training towards something that’s relevant in the story, this is exactly the time to talk about those elements of your setting. It still needs to be as concise as possible. You may be writing a fantasy epic with 300 pages of backstory dating back 100k years, but your audience only cares about that as long as an impatient kid being trained in the mystical ways of a lost monastic order will.
In short, teach your characters and your audience at the same time.