Our local pound shop sells cloths designed for drying glasses after you've washed them, however I find they're great for cleaning my screens, LCD or otherwise.

Just wipe the screen with a damp (not dripping wet) cloth, then dry with the glass cloth, simple as that.

I also use the same cloth (there were two in the packet) for cleaning my camera lenses & specs as well.

Well worth the pound I spent on it.