The best way would be to just use water and soft cloth. Even the inside of a babies diaper would do the trick. Also, using eye glass cleaning wipes could work.
A simple way to clean it would be to wipe the screen with a mild solution of soap and water, and wipe with cotton or a paper towel. There are also touch screen cleaning kits sold at many electronics stores.
You can use a screen cleaner or take a clean cotton piece don't sock into anything like water or oil like. Clean with the clean cotton piece. Better to put screen guard also.
There is actually a almost dry cleaner, kind of a paste, that will not harm the buttons or the phone. Just wipe it on and wipe it off. It will keep fingerprints etc. off your phone and improve functionality.
I would first turn the phone off since you don't want to be hitting buttons while cleaning. After the phone is off i use a little windex. You don't need much. Spray it on a terry cloth and gently go over the screen. Windex won't hurt it