Riveted maille has long been an elusive art, oft spoken of with much more difficult that it really is. In this essay, It is my intention to shed some light on a simple, effective method of producing riveted maille. Before I go any further, I would like to thank the following people: Stephen of Forth Castle, his study into techniques, as well as oft questions define the impetus for my interest; Eric Schmidt, he also shed some light ; both of these gentlemen frequent the Armour Archive   Sara Trice, also a good source for information, as her Sara's chain mail connection is a temple of maille.
    To make riveted maille via this method, you first need rings. Common wisdom says that one should use small (and therefore of high gauge number) wire, as the riveting process imparts quite a deal of strength. In the future this will occur. For this essay, i used what i had on hand, 1/2" inner diameter rings made of 11.5 GA galvanized hi-tension wire. This is about the worst material I could have chosen. First, the wire is wicked tough, second, it is heavy, and third, it is galvanized. DO NOT USE GALVANIZED WIRE Galvanized wire is made by the application of zinc. When this zinc is heated (more on that later) toxic fumes are produced. These fumes will KILL, so don't risk it. To make the rings, you need to coil the wire around a Mandrel (a round dowel, etc.) , then clip the coil with cutters. For smaller wire, I use a pair of highly modified needle nose pliers, I cut the noses off, and ground one side thinner, to fit inside a small (3/8") coil.
here is a picture (linked to a larger pic) of said snippers. For larger coils, i use 9 inch bolt cutters from the Great Neck Tool Company.
By twisting the cutters clockwise, causing the bottom jaw to press against the inside wall of the coil, i get a very clean cut. Here is what the rings look like: (linked to a larger image)
these are the rings I use for most of maille, my hauberk, coif, etc., It is a compromise in cost, toughness, and speed of assembly. The steel is, however, pretty hard, and requires annealing. This is accomplished (for ferrous metals) by heating to a glowing red, then allowing to slowly cool. I did this by stringing the rings on a piece of wire, and placing in a fire of charcoal (notably, my grill, after a weenie roast) I came back later (the next day), and retrieved them . They looked like this:

After this, the metal is much more soft, and can be easily hammered, bent, etc. Eventually the rings will need to be overlapped, and flattened, but i find it easier to do a "pre flatten", a step which some people consider unneeded. I personally feel it adds a small step, but makes a second step easier. To pre flatten, merely place on a flat, heavy metal surface (anvil, metal weight, railroad track, etc.) and strike the ends with a hammer until slightly flattened, thusly:

The next step is to overlap the rings. This can be done in a variety of ways, i personally use linesman's pliers. they have a circular hole in the backside of them that works well at keeping the edges round. After overlapping, the rings should look thusly:
At this point, depending on the wire type you used, It may be necessary to anneal again. I personally had to, but if you choose a naturally soft wire, you might not need to. After annealing (or next, if you choose not to) you will need to flatten the overlapped area. Some people so not do this, but for the maille to look authentic, the 2 overlapped parts must fit  into each other perfectly, a feat only accomplished by a post overlap flattening. If all is done well, and you did the pre flatten, a few hardy hammer strikes is all that is needed to produce rings similar to these:
The next step is to put the rivet holes in the flattened area. The choice of the tools depends on the type of rivet you plan on using. Two types predominate the historical examples, round, and wedge. I personally use round, if for no other reason that I own a drill, and could not afford the materials to make a wedge punch. According to Stephen of Forth Castle, a good punch (or more appropriately, a pierce(?) ) can be made with a few small modifications to a glass and tile drill bit (the smallest in a set commonly available at walmart) with a diamond cutting wheel attachment for a dremel tool. If you choose to do this, refer to his essay, which I am sure is coming soon. If you choose to make round holes, you have several options. A drill will suffice, though it can be slow and prone to wander, various punches can be had, including the whitney style, though I have never done this. Once the holes are made, whatever the method, you will need rivets. The wedge style is made by nipping small pieces of flat metal into little triangles. Again I refer you to Steven of Forth Castle. For the round rivets, some people use sewing pins, I personally use these:
You can pick them up at Wal-Mart, for around 2 bucks. Anneal them, I do this by pouring them into a metal ladle, and heating them with a torch, then allowing to slowly cool. Put them through the hole you made,  trim the length, and squeeze them between pliers. This will set your rivet. Assemble in the usual way. If you have never made Maille before, I shall refer you to the "Strangeblades and More" Animated Guide to Making Chainmail **her site shows you how in the simplest terms i have seen thus far. And, if all is done right, your effort should look like this::

That's it. It is my intention that this show you exactly how easy the process is, and will, hopefully, lead you to attempt it yourself. I can usually answer most questions via e-mail, but it would be my hope that this essay answers all of your questions.
 
 

**It has come to my attention that the proprietor of Strangeblades has removed said helpful and informative essay. it seems that she had several complaints ranging from the legitimate ("you've stolen my images", or "You've plagiarized my jewelry designs") to the absurd ("how dare you link my page!"). Sigh. Its a shame that its gone, but I shall leave the link up, so that you can read her side of the story.