How do you patent your own martial art?

I've spoken to my lawyer about this, because I know martial artists that threaten to sue people for "teaching their stuff". The short answer is no.

If you write a manual or produce a video or otherwise fix something into a tangible form - then that thing has copyright. That's the book or video itself, but not your style.

You could also file a trademark on your style name or logo. Krav Maga is famously going through trademark lawsuits.

The real issue with trying to protect a style is that there is virtually no Martial Arts movements you could make that don't already exist in some other style.