Draw a line segment.
Open a compass to a radius greater than half the length of the segment.
Place the compass point on one endpoint and draw arcs above and below the segment.
Without changing the compass width, place the compass point on the other endpoint and draw arcs that intersect the first pair of arcs.
Mark the two points where the arcs intersect.
Draw a straight line through the two intersection points.
This line is the perpendicular bisector.