Use your straightedge to draw the given segment AB. Place the compass point on one endpoint of the given segment.
Adjust the compass width to be greater than half of the given segment's length. With the compass set, draw an arc that intersects the given segment. This arc should intersect both sides of the segment.
The point where the two arcs intersect (let's call it C) is equidistant from both A and B. It forms a segment AC congruent to the given segment AB.
Use your straightedge to connect points A and C. The line segment AC is congruent to the given segment AB.