Clean both pieces of the leather you want to fasten. Use a quality leather cleaner, according to the directions on the label, to remove dirt, dust and grease from the leather.
Hold the two pieces of the leather together. Punch a hole through both pieces with a leather punch. Insert the copper rivet through both pieces of leather, and turn the pieces over so the rivet head is laying on a flat surface. The post of the rivet should be facing you.
Push a rivet burr over the copper rivet post. The rivet burr looks similar to a copper washer. Position the round-hole side of the rivet-setting tool over the rivet post and against the burr. Strike the top of the tool with a ball-peen hammer.
Cut the rivet post 1/16-inch above the burr with a pair of nippers. Nippers have curved jaws that cut through the post.
Position the concave hole of the rivet tool over the remaining post and against the burr. Strike the top of the tool with the hammer. Move the concave over the post, left to right, as you strike the top of the tool with the hammer. This rounds the end of the post over the burr.
Remove the rivet-setting tool and strike the center of the burr and post with the flat side of the ball-peen hammer.