Strategy 1: Do it once, the right way
Many campers believe in taking the time before driving home to dry out, wipe down, and pack up the gear so that it can go straight into storage from the car. If you go this route, it will take some time at the campsite to clean up anything that has gotten dirty. It helps to have a hand broom for dusting off dirt and disposable wipes or a damp rag for cleaning up gear. Some chores, like cleaning out the cooler, will need to wait till you get home.
Strategy 2: Deal with it at home
The other strategy is to simply get your gear into the car however you can, the idea being that it will be easier to dry out tarps when you can stretch them out in your yard or easier to clean dishes when you have your dishwasher (or at least hot running water) at the ready. If you have enough room in your car, you can loosely roll up sleeping bags and pads and air them out at home.
Dishes from the last breakfast can simply be placed into a container and washed later--your departure will be quicker, though you’ll need to devote some time when you get home to putting things in order.