Use a microfiber cloth. If there's dirt, spray a bit of water on the cloth first, then rub until clean. That's it!
OK, maybe it's a bit more complicated than that, but those are the key concepts to keep in mind. When cleaning any piece of electronics, you never want to spray water or a cleaning solution on it directly. Water and a bit of elbow grease are usually enough. For stubborn stains, you can also cut the water solution a bit with vinegar. If you don't have a microfiber cloth around, a soft piece of moistened paper towel will do as well.
The process is a bit tougher if you want to truly sanitize your phone's screen. For traditional LCD screens, you should never use an alcohol-based cleaner. But with glass touchscreens, you can get away with a bit on a microfiber cloth. Even Apple doesn't recommend using an alcohol-based cleaner, but if you step into an Apple store, you'll find workers using pre-moistened alcohol wipes left and right. Go figure, right? While I wouldn't recommend doing this daily, a quick wipedown with an alcohol-based solution is the best way to kill all the germs nesting on your phone.
I totally agree with Devindra: Microfiber cloth is the way to go. If you don't have one, a wet wipe from Grime Boss or similar designed-for-touchscreen napkin works as well. And if you're on the go and need something quickly, I find that most fabrics work well, as long as they are at least slightly textured. Ribbed sweaters or rougher napkins are good examples, and your shirt sleeve can work in a jiffy too. Not ideal, but good in a pinch!