There are 31 cars to be found in Jack Spots, and 10 Most Wanted cars, for a total of 41 cars. For discoverable cars, you'll find Jack Spots all over the city. Each car has 3 Jack Spots. There's also the 10 Most Wanted cars that need to be earned. Once every car is found and earned, use the "Change Car" option from the Easy Drive menu to get in and use each car at least once.
Progress can be tracked by viewing the cars in your car milestones under -> Driver Details. There's a "drive this car" milestone for every car, which should be completed if you've used that car. Also note that you only have to get in the car for it to count. There's no minimum distance required. I was able to unlock it without even turning the key in most of them.
See "Most Wanted Rides" and "Networking" for more information on obtaining vehicles.