To access the Vehicle Theft missions bring up your phone, click Saintsbook, and then Vehicle Theft. These missions involve you driving to a certain area and looking for a certain vehicle. If you drive around the area, you will see the vehicle icon appear on your mini-map telling you exactly where the vehicle you need is. Once you hijack the vehicle, you need to drive back to a certain point while police and gang members chase you down. This is very easy to do if you use notoriety wipe (or mayor's forgiveness) after getting in the vehicle. It is really only needed for the slower vehicles, but if you want to use it for all then you can do so easily by saving, quitting, and restarting the game and they will be available again without having to wait.
There are 30 vehicles you need to steal.