You anticipate as much as possible the motion of your subject and move or refocus as necessary to get the shot.
Like with anything, practice is the key to being effective. Lead the shot, that is, pre-focus ahead of framing and fine tune as you get the shot.
I generally have my lens at 3 or 5 meters depending what I'm after and I look to anticipate my framing before I raise the camera to my eye. Doing this, there's less to do when I take the shot.
It's not as easy to start at as with an auto-focus, but once accustomed, you can get shots that an auto-focus can't easily get, e.g. a subject sitting on a swinging swing.
Of course, with all that said, precise focus is not always an important feature of a photograph, particularly of a subject in motion.