A microfiber cloth is very good, even dry. There are several grains, so choose one made for glasses or screens rather than those hairy ones made for floors
For stains just a little moist like your breath can help, since they (hopefully) consist of dried saliva spread by a "check six" yell.
I was also very satisfacted to the results of 'AM One Touch Screen Cleaner'-kit, where the microfiber is stretched on a soft stick and assembled on a handle. Guess the large flat surface helps avoiding stripes. It also includes some cleaning fluid.