This game follows the basic racing game format where you compete in races and must win in first, second, or third place to move on. As you go through the races, you will unlock weapons, vehicles, and maps that let you go further into the game. Before each race, you will have primary and secondary goals clearly stated for you. The primary ones are mandatory, but the secondary ones are not. I highly recommend that you complete in as many of the secondary ones as possible before you move on too far, because those secondary goals unlock a lot of the really good weapons that you'll need.
The goals are basically the same for each set of tracks in that you either need to win a race, take out a certain opponent, or beat some kind of time limit. I found many of them to be crazy difficult, and I had to go through the same races over and over before I could beat them. However, I will admit that I've never been all that great at racing games, so maybe it's just me.