By chainmail in this context, I mean a style of armor created by numerous interlocking metal loops, a style used heavily in Europe up until it was rendered obsolete by gunpowder, as well as in Japan. The term chainmail, however, can also mean a written form of communication, propogated by post or email, intended to induce the recipient to reproduce and retransmit the letter to several new recipients; a kind of wetware virus. This writeup is about the former flavor of chainmail.
It isn't difficult to create your own chainmail clothing and accessories. Most of the tools you'll need are commonly available, and the supplies are cheap. You can make a bracelet or necklace in less than an hour. Chainmail clothing is more time-consuming, by necessity of larger size, but can be quite rewarding as well, although you're probably more likely to wear a chainmail bracelet in public than a chainmail shirt.
As far as raw materials are concerned, you'll need metal wire. The kind of metal and the thickness depend on your preference and the particular application. 14-gauge and 16-gauge galvanized steel wire is appropriate to start with and is available at many hardware stores. Stainless steel is better for jewelry, but you may need to order it. There are several retailers on the Internet specializing in wire. You can also buy pre-made rings from Internet suppliers, but that seems like cheating to me.
All you really need for tools are a pair of pliers (the exact nature of which is a personal preference; I find I operate best with one wide, gripping plier, and one needle-nosed moving plier), wire cutters, and a wooden or metal dowel ("dowel" is a fancy word for "stick"; the diameter of which determines the size of the rings). You can get these at any hardware store. Optional tools which are handy but not necessary are: a sturdy pair of gloves; vice-grips; high-end wire cutters such as Knipex's compact center-cut bolt cutters.
The overview is: wrap the wire around the dowel into a spring-shaped coil, then cut up the dowel, producing individual rings. Then, use the pliers to open the rings, attach them together in a pattern, and subsequently close the rings. Please note that this process is much modernized from the actual technique used by chainmail artisans back when chainmail was combat technology.
Making the coils is the most physically arduous task of chainmail-making. The goal is to wrap the wire around the dowel. (You should probably wear protective glasses while doing this, in case the wire slips, springs back, and hits you in the face. I have some nasty scars.) You will get a spring. Use the wire cutters to cut off each ring. The rings should be very nearly circular, with the ends not quite touching.
I find the vice-grip is very useful to hold the wire to the dowel while you rotate it.
There are several standard patterns, enumerated by Tsarren.