Bryse Wilson (of the Chicago White Sox) has pitched a ball to Trevor Larnach (of the Minnesota Twins). The Chicago catcher, Matt Thaiss, now rises and prepares to throw out a base-stealer (not pictured).
The Pitch is a Ball...
The pitcher pitches, and a runner on base takes a shot at a stolen base. The pitch itself results in a ball (but not a walk)1, and now it's time to chase down the base runner.
The strategy for defending against a stolen base depends very much on the situation; how many runners are on, which bases are under seige, those sorts of things. Ultimately, it comes down to the catcher, who may or may not throw down to the base in an attempt to get the would-be-thief out. Actually making a throw comes with risks; if the catcher isn't accurate, and throws the ball into the outfield, a run is almost certain to follow.