How do I cut a perfect square out of paper for origami folding?
This works better if at least two of the sides are parallel. It is required that one corner is at a right angle.

When I am trying to get perfect squares in paper I fold the paper in half diagonally. Not across the center exactly but more so that the two sides that make up one corner are brought together. Any paper that sticks out after that is removed.



In the above image the paper is fold from the bottom left into the upper right so that the top edge has no overlap. The grey is what would be waste.

Getting rid of that excess paper can be challenging as there is usually only a sliver at times. What I do is put a metal ruler down along the edge and use a craft knife. Start where the paper is thicker. Avoid moving the ruler even after the first cut is done. If you have to get rid of left over slivers or tufts you can usually take a few short passes without ruining the new edges.