Winding coils is one of the least speculative steps in making maille. Simply, wire was wound around a mandrel. The length of the mandrel is dictated by the length of the segments of wire available to the maille maker.
The earliest maille makers likely did not have access to long lengths of wire. Consequently it is believed that the earliest rings were wound on simple hand mandrels. E. Martin Burgess made such a tool:
It is worth noting that most authentic maille has a right-handed twist to it. If you consider the way such a hand mandrel would be used by right handed people (which most people are) then this is not surprising.
The later maille makers (including us!) had access to spools of wire. This allows us to make larger winding jigs. Below is a picture of my winding jig. It is very sturdy, and allows the use of different sized mandrels. Also, since one end of the mandrel is left straight, the jig can be cranked by a human or hooked up to an electric drill for speedier coiling.
If you use an electric drill to wind your coils, use extreme caution. If you get caught into the coil you can wind your fingers up into it very quickly, which is uncomfortable at best, and can mangle your hand at worst!
If you really want to make use of modern technology, you can pay a spring manufacturer to wind (and even cut!) coils for you. If you go this route, be prepared to shell out some money. It's not that the springs or rings are that expensive (I got mine for a penny a ring) - it's just that you have to buy a lot of them to make it worth the manufacturer's (and your) time. In order to get the rings below at $.01 a ring I had to order 50,000 of them - $500 worth.
The good news is that many of you will find that the time you save in not having to wind and cut 50,000 rings is worth the money.
I ordered my rings cut with the overlap built in. While this speeds my process (I don't have to overlap them myself) it results in rings that, when finished, are nearly perfectly round. This is not seen in authentic maille - generally authentic maille rings are somewhat oval or D shaped.