Teemo is a late game splitpusher with a lot of autoattack and spell damage, who is also a huge lane bully.
The first time I played Teemo I fell in love with him, and I haven't stopped playing him since.
I have discovered many different ways to play him well. The one I think is the most fun though, is AP Teemo simply because he pisses off the entire enemy team with his 600 damage shrooms, and autoattacks that do far too much damage. You can also get pretty much free kills with well placed shrooms. This guide should help you to play Teemo in the top lane and mid lane.
My summoner name is ParallelVortex (I don't know what I was thinking when I came up with my Solomid username) and I used to main Teemo, and still play him today!