In the video series below, you will find a number of methods for cutting (and sewing) 1/2 square triangles.
Introduction to Making ½ Square Triangles (#1 of 8 videos)
Making ½ Square Triangles Using Your Rotary Cutter (#2 of 8 videos)
Why Does the 1/2 Square Triangle Formula Require You to Add 7/8 of an Inch? (#3 of 8 videos)
Making 1/2 Square Triangles Using 1 inch Formula (#4 of 8 videos)
Why Add 1 inch When Making 1/2 Square Triangles? (#5 of 8 videos)
Sewing Diagonals BEFORE Cutting to Make ½ Square Triangles (#6 of 8 videos)
Mass Producing 1/2 Square Triangles (#7 of 8 videos)
Paper Piecing Strips of ½ Square Triangles (#8 of 8 videos)