Just complete the lists from the five chop shops in the game, delivering the cars to the nearest chop shop to where you find the car.
To help you in your journey, complete the Suburbs Fuzz activity to have your police notoriety reduce quickly. On some of the cars, it can make a one-star wanted level disappear into nothing and a three-star go down to a two quickly, which really makes a difference, especially when you go to get the weakly-armored, slow Delivery Truck from Saint's Row.
If you are having trouble jacking cars for the lists, either create a road block with a large vehicle such as a bus, or take careful aim with a pistol and kill the driver, both of these tactics will be hard to achieve if they are not done right the first time you try--if you fail to stop the car or its driver, the driver will freak out and if you cannot catch up, the game will make the car disappear since it vanished from the view of the camera.
And remember to SAVE OFTEN. This mantra can't be repeated enough with Saints Row in general, but especially since the game does not autosave at all during this activity, it's important to save either after every delivery or after the really tough ones.
(Thanks Gnemlock!) Steal cars and store them in your garage, which may be closer than the nearest Chop Shop and can be delivered with a simple phone call to the car delivery homie.
(Thanks Spoilt8!) Complete all levels of insurance fraud -- this unlocks unlimited sprint, giving you a better chance to keep up with vehicles.