Destruction Means Nitro
You can reach really high speeds by using nitro, but it takes time to refill. You can speed up the process by smashing into destructible objects such as barrels, crates, and fences. You can also ram your opponents, if you're going fast enough, for the same effect. It's best if you can chain together all sorts of chaos to really get your meter going.
Drift Secrets
As you round corners, you can brake at the same time you make a hard turn to launch into a drift. While you are drifting, your nitro meter will gradually refill. You can refill it even while you're in the process of boosting. Therefore, a good technique is to boost just ahead of a turn, then immediately start drifting through the turn while your boost is going. This will have the effect of allowing you to drift much further distances, since your nitro-consuming boost is counteracted by the bonus you receive for drifting.
Earning Card Boxes
You can earn card boxes if you obtain all of the stars for a given season, but there are other possibilities, as well. Make sure that you're competing in multiplayer races every day. Win three of them over the course of a day and you'll receive a card box. Of course, you'll need to monitor your oil, since racing against your fellow players earns up racing just as quickly as racing against AI opponents.