Modern touchscreens tend to use an oleophobic (basically, oil-repelling) coating to help reduce fingerprints and smudges, but a lot of people don't realize that this requires special care to ensure the coating lasts as long as possible. In fact, you may have noticed that your screen seems to collect smudges much more easily over time and this is likely because you've worn off the oleophobic coating.
As with any screen, only use a soft, lint-free cotton or microfiber cloth to wipe your touchscreen. Make sure not to rub too hard and try wiping only in a one direction in an attempt to just brush the dirt off the screen - if this fails then try wiping in the perpendicular direction before resorting to using small circles but note that these can more easily scrub off the coating.
The most important thing is never to use cleaning products on your screen. If a dry cloth isn't working then dampen the cloth with a small amount of water and try again, and if this doesn't work then try a 50-50 mixture of water and white vinegar. -Jeff MacArthur