Multiplayer mode
There are two challenges in multiplayer mode. The standard challenge costs 100 credits to enter. The pro challenge costs 300 credits, disables the steering and braking assists, but has a larger reward. Multiplayer mode also has a ranking system. Winning a race will result in winning RP (ranking points), while losing a race will decrease your total RP by a large amount.
Upgrades
You can upgrade each car in four different ways. Top speed upgrades the maximum speed of your car. Acceleration decreases the time required to reach top speed. Handling makes turning sharply easier. Brakes will allow you to stop quicker and make sharper turns. Follow the recommended upgrades listed before entering a new single player race to get tips on what work needs to be done on your car for a better chance of success.
Various strategies
Leave the steering and braking assists turned on until you learn the controls. You must brake to the correct speed in order to make sharp turns. Take note of how steering and braking assists work during those turns to learn how to do it manually. Play campaign mode to earn credits to afford new cars and get stars to unlock more cars for purchase.