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)
Step 2: Grind the Electrode
Do this, especially if the rod is a brand-new cylinder and doesn't have a pointed or rounded tip yet.
The tip will become rounded due to heat as you weld.
Lincoln recommends a balled tip for AC welding, and a pointed tip for DC welding.
The pointed tip will give a smaller, more directed arc. The arc will tend to dance around, when from a rounded tip.
Step 3: Insert the Electrode Into Its Collet
The tip of the electrode should be about 1/4" away from the protective sheath, but not much more.
Skip this if you already have your electrode ready.
Shown below are two different types of electrode holders.