Just a quick tip. A lot of screen protectors and cases come with a "silk" or "soft" cloth to clean your screen. You may notice that these clothes smear more than clean. Something I found to work much better is a microfiber cloth. I use microfiber towels to detail my truck(mostly to polish), but I find that they also do an equally great job at keeping my tablet clean. Microfiber towels are generally pretty cheap, I just bought a pack of 10 from the local auto store for $10. They're much bigger than the little cleaning clothes that comes with the protectors, so you may have to cut them down to a more appropriate size.
All the work of the same cloth.
Just be sure to move it in circles.