Constructing the midpoint of a segment
Constructing the midpoint of a segment is probably easier than any other straightedge construction.
Step #1: Use a ruler and a pencil to construct a segment of any length on a piece of paper as you see it below
Then, fix your compass opening to a distance somewhat bigger than 1/2 the length of segment AB.
You should open your compass large enough, but make sure that the distance is not more than the length of AB.
Step #2:
Put the needle of your compass at A and draw an arc
Put the needle of your compass at B and draw an arc
The two arcs should meet as shown below:
Step #3:
Draw a line joining the two points where the two arcs intersets
The point of intersection of the line and the segment shown with a green point is your midpoint