place the center of the compass at A and extend the compass to point B
draw the circle with center A and radius AB
now move the compass center to point B and draw the circle with center B and radius AB
the two circles will intersect at two points ( you don't really need to draw the entire circles, just enough so that the arcs you draw will intersect in two points)
use a straight edge to connect those two points of intersection, and the line you draw will be the bisector of the given segment AB
( the common radius of the circles you draw doesn't actually have to equal AB, it just has to be greater than one half AB in order for the circles to intersect each other. But the proof that this construction works is a little more elegant if the radii are AB)
