The first thing you need to make the task of teaching cleaning skills a little easier is buy-in from your teens. How do you get this? Try making learning to clean and doing chores a little bit fun. Is your teen inseparable from that ever-present MP3 player? Encourage him or her to take it along on their chores. Or pump the house stereo and jam out together while you're scrubbing the tub. If you have multiple teens, you could create a little friendly competition by assigning chores points or scoring their finished product. The winner could be exempt from the chore they hate the most for a week or receive some other treat or reward.
It's also important to make sure your teens completely understand each task at hand. During the teaching process, have them shadow you a couple of times. Then, when it's their turn, have them explain to you what they're doing and why. You might even want to check in on them the first couple of times they're on their own. You should make sure they know enough to not run after you for each step with questions, but encourage them to come to you with any questions that due arise, so you avoid unfixable mistakes like ironing silk or bleaching your carpet.
Work your way up to the complex tasks. If you're starting your teens young, increase their responsibilities each year. Or, if they're older, add a new, more complex chore after they master each skill. Vacuuming could be first, followed by dusting and then finally washing the floors. In the laundry room, start out with folding, and then move to ironing and loading the machine. You might want to save the bathroom for last. Begin with the floors and the shower, followed by the counter, mirrors and faucets. They can work their way up to that scary toilet. Once your teens start getting the hang of more and more skills, creating a chore calendar will help them keep track of what they completed and what's still on the to-do list for the week.
Finally, make sure you encourage and compliment your teen. Positive reinforcements will help make them more confident in each skill. And, compliments and thanks will help them understand the impact they're making on the family unit. This will add to their "buy-in" and the lessons of responsibility and obligation they're learning.