If I wanted to become a Vita dev, what would I have to do?
And what would I have to know?
You could become a PlayStation Mobile dev. That's the simplest route, since Vita supports PS Mobile. Also the cheapest option. PS Mobile games can be exclusive to Vita.
Or you could directly develop for Vita, in which case you'd need to sign up here: http://us.playstation.com/develop/ The static IP address is a must, but you don't need it when registering. This is the more expensive option.
As far as knowing things, just learn an engine. With PS Mobile there are lots of free engines you can use (including unity). With direct Vita development you can still use a lot of the same engines, but there's a lot more behind the scenes you have to do. It takes time more than skill though.