To install rivets you should have a rivet set which is a rectangular punch. The working end has a hole the same width as the rivet and beside that is a round divot that your rivet head should fit into. You place your rivet through the metal parts and then insert the hole in the rivet set over the end of the rivet that sticks out from the metal you are joining. With the head of your rivet on something very solid tap the hole in the rivet set down over the shaft of the rivet that you have sticking up. This will cause the end of the rivet set to contact the pieces of metal you are joining and squeeze them tightly together. Next pull the rivet set off the rivet and position the round divot on the end of the rivet and hammer it down on the stem of your rivet to form the round mushroom shaped cap out of the stem.
You can see a rivet set in post #1035 of this link:
http://www.garagejournal.com/forum/showthread.php?p=2512802
Photos 9 through 15 of that post have shots similar to what you are doing. Photo 10 shows a proper rivet set but to the right beside it you can see the end of another one that is a homemade one. It was made by drilling a hole the size of the rivet stem and beside it a round divot was drilled with a larger drill and rounded with a burr until the rivet head fit inside. They are easy to make with a piece of flat bar.
