I have thousands of Prestige and no idea what to do with it. I have read that you can spend it on actions, but I can't figure out which actions those are or where I find them.
The main purpose of Prestige is to add to your Dynasty Score: this shows how powerful and successful your dynasty is. If your final Dynasty Score is higher than your buddy's Dynasty Score, you're a better ruler than him. You are usually going to get a lot more Prestige than you can spend over the course of a ruler's life.
That said, there are a few things you can spend Prestige on, though none of them are particularly expensive, unless you're a new ruler of a young dynasty or otherwise poor in prestige:
Though it's not an action, remember that you get an opinion bonus of +1 per 100 prestige, that applies to everyone. It caps at +20, but it's still quite useful!