The first technique (used on the Balkan Puzzle) was to add 2 inches to the size of the finished square and then sew the two fabrics together all along the outside of the square (all four edges at once) then you cut it on both diagonals. You end up with 4 squares from one, already sewn together after you cut it.
The second technique (which I like the best) was to add one inch to the finished square (even though you only need 7/8 inches added) then draw a line on the diagonal of one of the fabric square backs and sew the 2 fabrics together a 1/4 inch on each side of the line, then cut along the line. You end up with 2 finished squares, but what I really liked about it is that you have to square it down to the finished size which makes them come out as perfectly finished squares. Sometimes when making the half square triangles the old fashioned way, they come out wonky. This makes them perfectly shaped!
Anyway, here are the photos: