I had lots of questions from patrons of the show last two weekends about armor and the Middle Ages, and while the process I use is similar to what was done historically my butted mail isn't what they used. Butted mail is created when you close rings so that the ends are butted against each other. This picture is a good example of a piece of butted chainmail.
If you were wearing armor for defense, you wanted riveted mail. The ends of these rings overlapped each other, were flattened, and a hole was punched through so each ring could be riveted together. This made the piece stronger and much less likely for the rings to unintentionally come apart.
This site gives a simple and interesting explanation of different types of armor and how they were created. It's amazing how labor intensive it was, and still is, just to make a single piece of armor.