You don't really notice the fingerprints when the device is showing a bright screen, but the fingerprints and smudges are very visible when you're using an app with a dark background or when the screen is off. Some users call their iPad already a magnet for fingerprints.
The iPad User Guide suggests using a soft slightly damp cloth, but please make sure not to allow moisture in any of the openings of the iPad. You can also use your sleeve to wipe off any smudges on the iPad screen. "If you still have a smudge, add some moisture with a puff of breath and rub a bit longer without the pressure", Apple suggests.
Do absolutely NOT use any window cleaners. These cleaners can damage the oleophobic coating on the iPad screen, which can lead to reduction of functionality of Apple's iPad over time.
Cleaning your iPad screen every time you use the device gets old. The best way to prevent smudges and fingerprints on the screen (and scratches as well!) is a protective shield. Most protective shields available on the market also significantly reduce a large amount of glare, which also ranks high in the iPad complaint list. iPad protective shields are available in online- and retail stores, starting at $10.
To keep the outer areas of your iPad clean and safe from scratches, it is a good idea to purchase an iPad case. There is a huge selection of iPad cases available on the market, with new cases being announced seemingly every day, in all kinds of materials and colors, for every kind of budget.