Teens, often absorbed in their own world, don't see what the big deal is or think they don't need to clean their rooms because they are the only ones that sleep in it. No matter what your teen thinks, he should understand that as a parent, you make the rules that he has to follow. Making this completely clear, along with your expectations and consequences for not cleaning up, are the keys to getting your teen to starting cleaning up his mess.
Write down your cleaning expectations. Your teen will look for ways out of consequences by claiming you were not clear. Write down the rules for cleaning up after yourself and make copies to put them in areas of the house that your teen frequents. If cleaning up after meals means putting your plate in the dishwasher, for example, write it down plainly. Write down that cleaning his room includes vacuuming and hanging clothes in the closet, if that is what you expect.
Make the consequences clear. Your teen should know that for every instance of not cleaning up after himself, he can expect a consequence. Stay absolutely firm on this to get the point across. If you decide to remove his TV privileges when he doesn't clean up after himself, do not give in "just this once," if he pleads with you. Otherwise your teen will start to think they can get away with breaking the rules.
Never clean up your teen's mess under any circumstance, even after giving your teen a consequence. Make him do what he should have done in the first place and clean up the mess he made.
Practice what you preach. If you do not model cleaning up after yourself, you can hardly expect your teen to do the same. He will not hesitate to call you out on your messy and hypocritical behavior, so don't leave the newspaper you just read strewn on the coffee table. Hang up your coat in the closet, rather than tossing it on to a chair when you get home.
Take extreme measures when absolutely necessary. If the regular consequences are not having an effect on your teen, let him know that you will turn your problem into his problem. For example, If your teen constantly leaves the table without putting his plate in the dishwasher, leave his dirty plate, cup and utensils right where they are until the next meal. He will have to wash it himself and re-use it to enjoy dinner. If your teen keeps leaving his wet towel on the bathroom floor, he can no longer use the towels. Make him buy his own with his allowance, and if he leaves that one on the floor, take it. It is your bathroom and those are the rules.
Negotiate within reason. Teens often have hectic schedules, which can make it tough for them to maintain your cleaning expectations. If cleaning up his room is the major issue, talk to your teen about establishing a cleanup day once a week, when he has time to do a thorough cleaning, provided he at least keeps the clothes off his floor during the rest of the week. If he has a particularly busy week, allow him to negotiate for easier or quicker chores with his siblings, such as taking out the trash instead of mopping the kitchen floor.
Talk to your teen. Teens often think parents just want to nag them about doing chores for no reason. Have a heart-to-heart with your teen to explain that you are trying to prepare them for a future where they will have to share their living space with others. Not cleaning up after himself will show a disregard for his roommates and their shared space. Explain that it also makes you feel he has little regard for the upkeep of the home that you and your spouse worked hard to provide for him and the rest of the family. Helping him see the issue from your perspective might make him think twice before walking away from his own mess.