In this game you can find several types of races. Water, off-road and street ones. The best suited character to this job is Franklin, due to his very useful Special which makes easier every hard turn. What is more, on he can take part in night street races in Los Santos.
The general rules are similar for every race. To get a medal, you have to finish it in the first three places. But you can't fire at your enemies or try to blow them up. You can push them, what they will also try to do. You have to also get through every checkpoint. In most of cases (besides street races), you'll get a vehicle which you will control, so you don't have to run around whole San Andreas to find a proper vehicle.
First of all, remember that racing in GTA isn't similar to Sonic Racing. Speeding up constantly you'll surely get out of the route and break. If you burn the gum before the start, you slow down your vehicle and there are no accelerators on the route, nor bonuses. Drive carefully and calmly, avoid accidents. If you crash at the start, don't cry - computer players also make mistakes, so you may have a chance to catch up with them. Try to avoid too much pushes. Drive in a safe distance from everyone and notice symbols on checkpoints which inform you about the next turn. Try also to find various shortcuts through grass or parks. In water races you can also lean the scooter back to jump on waves. It's slower than normal driving, but you may be able to jump over obstacles and other players. You'll quickly discover that races in Grand Theft Auto V are not too challenging if you only have a proper car, drive carefully and use Franklin's Special.