You should clean your UV filter about as often as you would clean a camera lens -- not very often. Both filters and lenses can accumulate quite a bit of dirt before the imaging ability will be significantly degraded, and you're likely to inflict more damage with smudge marks from cleaning. Optical glass, while harder than most metals, is softer than sand and the silicate materials that make up most of the Earth's crust, so if you rub a tad too hard, you're likely to scratch your filter or lens. Instead, blow or gently brush dust off the optical glass.
If your UV filter does get really dirty, or it accumulates a residue of something like sea spray or an oily fingerprint that won't come off with blowing or brushing, then do what you must. Some camera manufacturers make special cleaning devices, such as Nikon's Lens Pen, which combines a brush and a microfiber pad for lifting greasy marks from optical glass. Zeiss and other companies also market special lens cleaning solutions that can also be used on filters. If you're going to use a cleaning solution, administer it with a special soft lens cloth, which itself should be washed between each use [source: Atkins].
For more information on photography dos and don'ts, visit the links on the next page.