The only difficulty is to create Perpendicular lines.
One possible way could be, if you are precise enough:
lets suppose the vertices are (P1,P2,P3,P4), where P1 and P2 are given two points.
Join the two points(P1,P2) and extend on both sides.
To draw a perpendicular at point(P1) on the line: Mark two points on the line equidistant from P1 on both sides, then place your compass at the marked points, there after create arcs using your compass such that they intersect.
joining the intersection of arcs and P1 would give you a perpendicular line on the given line.
Since you have created a perpendicular line, then it's not difficult to create a Square from it.