TIG can be used to weld copper, titanium, even two dissimilar metals, and is handy for making tricky welds (e.g. s-curves, or welds on round things)..
TIG generates heat via an arc of electricity jumping from a (tungsten metal) electrode to the metal surfaces you intend to weld - usually aluminum or steel.
TIG stands for Tungsten Inert Gas, after the tungsten electrode, and the sheath of inert gas (argon or an argon mixture) surrounding it.
Big thanks to Mose O'Griffin, who narrated, taught, and demonstrated.
Also, If you're interested in MIG welding, see this instructable:
Step 1: Choose the Electrode
For aluminum, the best choice is a pure tungsten rod.
You can alternately choose from any number of tungsten alloys (including thoriated tungsten - which is radioactive!) which are uniquely suited to welding particular alloys of metal.
For reference, this example uses the specific alloy 6061 Aluminum (the "steak and potatoes" or "normal" type of aluminum)