On the menu bar, find the link that says Actions. Under that, there is a link that says, "List Race Range" click on that link. This will show you all the drivers that are in the game. The ones that are in green are currently online. You can then choose your opponent. When you find which vehicle you want to race, click on the users name and under their details you will find a link that says, "Challenge this driver to a race" and click on it. Then the screen will prompt you with, "How much would you like to wager on this race?" Enter a dollar amount you are willing to risk. Then beneath that it asks, "How many turns would you like to spend preparing your vehicle?" Enter your turn amount. Once again, using more turns doesn't ensure you will succeed, however it may help, so be careful.
If you win, the dollar amount will be added to your bank roll, if you lose it will be deducted. If you challenge somebody that does not have enough cash to cover the wager, then they will decline your challenge and no funds will be transferred.
Keep in mind, that if you win a race, your pimp factor goes up, and if you do not have fuel or cash on hand after you logout of the game and someone challenges you, you will lose pimp factor and model happiness points as well. So make sure your car is racable when you log out.
Like stealing, you can get caught racing as well, and equally fined in cash. So be careful.
Also note that you can only bet a dollar amount if the person you are racing is currently online. If they are not online, then you can only race them for import models. The winner takes some from the loser and vice versa, the amount of Import Models that exchange hands is dependant on the losers model happiness.
You are limited to who you can race - only people in your Race Range. Your Race Range is determined by your networth and those players that are in the same networth range as yourself.