Good character/part combination is mandatory, you need good speed to keep up with or pass the pack and good acceleration to get moving when you get hit.
And of course, just getting better at the game. The more you play with GAF (or other good lobbies) the better you will get. You'll naturally pick up on what other players do and implement that into your own playing to keep up. You might not notice yourself getting better, but when you go back to the AI even 150cc seems like a complete joke that has to cheat just to keep up.
Ok thanks for the tips. Time to get practicing!