Learn to power slide, it's key to victory. Basically you hit R shoulder to hop into a turn and continue to hold R. As you're sliding (and steering to the inside of the turn), steer to the outside then quickly back to the inside. If you do it right you'll see some blue sparks pop out of your wheels. Do it again and you'll see a steady stream of orange sparks. Now just let go of R and you get a mini turbo boost. You really can't do anything without this, so learn to do it in every single turn and as many straightaways as you can get away with.
The drift stat on each kart controls how you slide. Karts with higher drift ratings will be able to steer tighter, and a lower rating will mean flatter turns while sliding. I actually prefer a low drift, but high handling on karts. The egg is my favorite currently.
Also, you should probably play through the offline stuff first. It'll help you get better, help you get used to being jewed by retarded amounts of blue shells, and it'll unlock new characters and karts to use online (like the robot).
tw