The term "chainmail" is actually relatively new. The armor used to be called maille, which I have from one source is/was a French term meaning 'to knit. At some later point the name was lengthened to chainmaille, and then shortened to chainmail. Most chainmaillers use the two oldest spellings, at least when conversing via written word among themselves.
Chainmaille was made by drawing a hunck of metal through a set of progressively smaller holes shaped like conic sections, so as to produce wire. This method of making wire also strengthened it. Then, as today, the wire was wrapped around a round metal bar (called a mandrel) in a coil, and links were cut from the coil. You take the links and close them with a pair of pliers in each hand.
The earliest chainmaille came about sometime around 300 c.e., and was first made of bronze; and then later steel as metallurgy advanced. I do not know in what part of the world maille was first invented; but it was in use in Japan and eastern Europe, and perhaps Persia as well.
In the past, each link was actually rivited shut, which added a huge amount of time to the already time-consuming task, but also added strength. A suit of maille cost a year's wages for an entire small town in Medieval times. Rivited mail is rare today, and costs upwards of $600. Butted mail, which is what you get if you just close the links, is pretty much standard now. Butted links are strong enough to hold together without being riveted, but will require more repairs if used in combat. Historically, butted mail was used for battlefield patching until the maille could be taken back to the forge for riveting. Soldering the links shut is a recently-used practice, and about as time-consuming as riveting.
Knitting chainmaille requires a good amount of patience, and natural and/or trained dexterity. You also need two pairs of good-quality spring-loaded pliars, and a source of rings. The latter can be had online, or you can roll and cut your own. I will let someone else detail this process, as I prefer to buy my rings rather than roll and cut them myself. Instructions, which require visual aids, can be had online; or if anyone wants to make a trip to Austin, TX I will happily meet you at the local gaming store and teach you.
How well a given piece of chainmaille can stand up to combat is determined by five things:
1. The weave
2. The inside diameter of the rings
3. The gauge of the rings
4. The metal from which the rings are made
5. Whether the rings are riveted, butted, or soldered
The thicker the gauge and the smaller the ID of the rings, the stronger the maille will be. Carbon steel is one of the best metals from which to make maille, and titanium ranks right up there with it. Unfortunately, niether of these is very practical, since carbonized steel tends to be hard to work with (either that or your start with mild steel and have a blacksmith carbonize the armor when you're done making it), and titanium is about ten times as expensive as steel.
Stainless steel, galvanized steel, copper-coated steel, and mild steel are all quite close to the previous two, so long as they have a good temper (say, half-hard).
Bronze is denser than steel, but not as strong. It must have the proper temper in order to be useful as armor. The same goes for brass.
Copper is way too weak in my opinion to be useful as armor, but would make nice jewelry or costume pieces.
Sterling silver, gold, and gold-filled wire makes beautiful jewelry but can be expensive and somewhat weak unless you get it at half-hard temper.
In the node for each weave, you will find information on what gauges and ID's are good for armor, costume pieces, etc.
Persian Weaves (no one really knows if these are truly historical Persian weaves, but somehow the name got attached):
Full Persian or Persian six-in-one
Half Persian four-in-one
Half Persian three-in-one
Weaves of unknown origin:
Birdcage or Byzantine
Pieces of armor you can make out of maille:
The weave links are under construction as of 4-10-01.