Grand Prix matches consist of 4 races. Each player earns points depending on what place they came in. Coming in first place earns 3 points, second place earns 2 points, third place earns 1 point. Fourth place earns nothing. The player with the most points at the end of the four races wins the Grand Prix. Win five Grand Prix races and the achievement will unlock. This achievement can be boosted, so check the Achievement Trading Thread for boosting partners.
If you are actually playing online, don't get discouraged if you do poorly in the first race, you can still come back from that. If you end up tying with someone, whoever did better in the last race will finish ahead of them. So for example, if you are one point behind someone going into the last race and you come in first and they come in second, you will have the same amount of points. But since you did better in the last race, you will win overall.