Go to multiplayer press to open easy drive. From there each mod will tell you what you must do to unlock it.
Jump Nitrous: Smash 20 billboards.
Jump Nitrous PRO: Smash 50 billboards with Jump Nitrous during SpeedLists.
Drift Tires: Record a 200 yards Drift 20 times.
Drift Tires PRO: Record a 1000 yards Drift 80 times with Drift Tires during SpeedLists.
The base version of each mod can be unlocked in a private multiplayer game by yourself. The PRO version of each mod will require at least one other person in a Friends or Public game with a SpeedList active. It's easier to do in a Friend game, where you can invite a player, start a SpeedList, and focus on earning the mods and ignore the objective.
The new Airport area is an ideal place to earn either of these mods. There are big open spaces to drift, and a high amount of billboards in a condensed area.
Find players in the Achievement Trading Thread.