Once a batter becomes a base runner, he doesn’t have to wait for his teammates to hit him around the bases. If he wants to take a risk, he can quickly travel around the bases himself.
The first thing he is going to do is get a lead off, which is simply taking a few steps closer to the next base. In order to make sure his lead isn’t too big though, the defensive team will hold him on by placing their first baseman (if the runner is on first base) at the base. The pitcher then has the option to throw the ball to the first baseman, rather than the batter, in the hope that the first baseman will catch the ball and tag the runner out before he can return to the base.
As soon as the pitcher decides to throw to the batter, however, the runner has the option to run to the next base. He must be quick though, because once the catcher receives the ball from the pitcher he will attempt to throw the ball to the base the runner is attempting to steal. If tagged before he makes it to the base, then the base runner will have been caught stealing and is out. In the event the runner beats the throw, however, he will have successfully stolen a base.