I am sure that most of you have seen this method of creating half square triangles, but perhaps those new to quilting have not. the pictures below, I hope, show how it is done very clearly. I made enough half square triangles for a full size quilt in one long afternoon - that includes cutting, sewing, ironing and squaring up the blocks.
two squares, right sides together, sewn on all four sides
cut on the diagonal
4 half square triangles.