Lots of pics and experimentation! Watch the mouse for a bit and feel out his tics and patterns, then start anticipating them. If you have him on a blanket and he tends to crawl under a certain fold at a certain spot, keep your camera aimed at that spot and wait for him to come. Eventually he will, and you can snap the pic. Don't try to chase him with the camera 'cause, lets face it, it just doesn't work, and nobody cares to see mouse butts anyways. Anticipation and guesswork is key. Settle down and prop your camera up and aim it at a spot, and wait for mousie. Maybe keep the focus settings on the mouse at all (or most) times so when the mouse suddenly stops moving to groom his face, start snapping some pics. By the time you get the focus settled on him, he may already be off and moving again (SO annoying, by the way
Or set some food down or a new piece of furniture, and start taking pictures when he pauses to check it out. Maybe your mouse gets wild and excited at first ("Freedom! New things! Eeek!"), but maybe he calms down after a while and just sits there chewing a seed. That's when you pick up the camera and start taking pics.
Take lots and lots of pics. It may feel like a waste of time, but when you get even 3 or 4 good pictures out of the bunch, it's totally worth it. When you get the hang of getting good pics, you can start trying to get "artsy". A good rule of thumb for pet pics is to get down to their level to take pics (don't stand at your full height and take pictures almost straight down to the floor). With mice (and anything, lol), I like to sometimes take pics from underneath the mouse (or cat or dog). Kind of gives them a Lordly, Godly look, like they're pondering their life and/or observing their kingdom.