After extensive use, you may find that your iPad screen is filled with finger marks.
As with cleaning any electronic device, first powered the device off and unplug any cables or accessories (including removing the power/sync cable). For those who usually let their iPad sleep, the proper way to shut down completely your iPad is to hold down the on/off/sleep/wake button for a few seconds until the “Power Off” red slide appears. And then slide the slider to the off position.
To clean your iPad, make sure that you do not use any window cleaners or any chemicals. Do not use any abrasives. The screen is a touch sensitive screen with an oleophobic coating. Oleophobic means that it is designed to repel oils (as from your skin). Abrasives will damage this coating.
Using a soft cloth to clean the screen will suffice. A dry cloth should work. Or you can add just a tiny bit of water or moisture to the cloth. Ideally you should use a lint free cloth. You can wipe the fingerprints off in a circular motion. Or actually any motion you like, as long as you do it gently. And making sure that you do not get any water or moisture into any of the electronic ports.
Here are the official instructions for cleaning your iPad screen from the iPad 2 User Guide at http://manuals.info.apple.com/en_US/ipad_2_user_guide.pdf on page 35:
“Use a soft, slightly damp, lint-free cloth. Avoid getting moisture in openings. Don’t use window cleaners, household cleaners, aerosol sprays, solvents, alcohol, ammonia, or abrasives to clean iPad. The iPad screen has an oleophobic coating; simply wipe the screen with a soft, lint-free cloth to remove oil left by your hands.”