On the topic of Diana, if you're having trouble dodging her Q, remember that it ALWAYS arcs counterclockwise. Stand on her left side and it's way harder for her to hit you with it.
This actually makes her the only champion in the game (that I'm aware of) with a mechanics-based handicap based on which team they're on. For example, on Dominion, blue team's Diana can easily use Q to check the side bushes on bottom lane and purple team's Diana cannot.
Diana
I haven't played her, but just read this bit of advice for playing against her:
"Be bold, and mighty forces will come to your aid."