It is bound to happen, your car ceiling will get dirty, making you wonder how you should clean it.
Purchase a fabric cleaner meant for vehicles and along with a microfiber cloth, scrub the ceiling of your car.
After letting the car fabric cleaner sit, (Always follow the instructions on the bottle), scrub the entire ceiling with a soft cloth.
For tougher spots, use a concoction of vinegar and water and some muscle and scrub that dirt away!