This is the simple bit, each car has 5 new events to complete. There are four cars available from the start but the Hennessey Venom GT Spyder events will have to be completed once you have got the Snake Bite trophy. These consist of races and speed runs. The speed runs require less average speed than before (such as Needle Point, the Hennessey is the fastest car but requires less than the Bugatti) so do not go full speed. It is better to not crash as your average will go down considerably after a crash. To access a race press then go to races, then select again and choose one of the five races you want to attempt.
All events marked by the Ultimate Speed icon (flaming wheel) as well as all events from the original game for each DLC car must completed, however, you do not have to complete the races from the other DLC packs that also may appear on the Events list.