We are lucky that Apple had the smart thinking to make the iPhone's touch screen out of glass instead of the plastic that was almost universal before the dawn of the iPhone. Unlike plastic screens, glass screens don't scratch and are incredibly clear and readable even in bright sun light. The reality of a touch screen phone is that it's going to have finger prints all over it and may even have some facial oil from holding it up to your ear when making calls. Fortunately, the screen is easy to clean. You can confidently wipe it off with a towel or even your shirt sleeve without fear of accidentally scratching it.
The glass surface is tough and is very hard to scratch with anything cloth. There are few times when you should need to use anything other than a soft clothe. You don't want to use window cleaner or any harsher cleaners on the glass since it could damage the surface. A few companies make cleaning products that are specially approved by Apple for cleaning the body and touch screen of the iPhone. These come in single-use wet clothe packages, or in a spray bottle that can be used multiple times. This is the ultimate way of keeping your phone clean but keep in mind that they are not actually for the great majority of cases: just use your shirt sleeve! Apple did its best to make the phone as durable and low maintenance as possible and therefore nothing special is required to keep your screen free of fingerprints and dust.