What do I need to know before painting a small room?

I want to tackle my first painting project this weekend. My bathroom has gone through three or four aborted paint jobs before I lived here, so the walls and the trim are a mishmash of colors like off-white, pink, and burgundy. The cabinet under the sink is made of fake wood laminate and was badly painted over with white. I’m thinking of painting the walls a deep shade of turquoise with white or off-white trim. What should I do before I begin?