Because I do many of these jobs by myself, I do the car in quarters (plus the hatch area if applicable last).
I remove the mats and slide both seats forward.
I grab my leather cleaner/conditioner (if necessary), plastic/vinyl cleaner/conditioner, vacuum hose, kneepad, carpet shampoo, scrub brush, assorted brushes, terry towels, put them in my bag and head to the rear of the vehicle.
I then vacuum the carpet and a little more than half the back seat. I then shampoo the carpet and the seat until all staining is removed. If the seating is leather, I clean and condition the leather. I scrub all the plastics clean. I do the back of the front seats at this time as well. I do the rear of the center console.
Then I go to the other rear seating area and repeat.
I then go to the front seat on that side, slide the seat back, and repeat.
Then move to the front seating area on the other side and repeat.
Vacuum and shampoo the mats. If they're rubber, I treat them with the cleaner I use on tires and scrub them with a stiff brush and water. I save the rinsing for when I rinse the car after washing.
If the vehicle has a hatch, I then do that last.
I deodorize the vehicle and the mats and then reinstall the mats, touch up anything that I may have missed, revacuum quickly to make it look perfect and call the inside done. If I'm washing the car too, which I usually am, I close it up and do the outside.
I get very good results using this method and it is also extremely fast because I'm not spending a lot of time retracing my steps. At first it seems daunting to complete all the tasks in one section, but after you've done it a few times there's a real good flow to this method.