Choose the appropriate filler metal. It must have mechanical properties similar to those of the base aluminum that you are welding. Ideally, use aluminum of the same alloy as the base metal that you are welding.
Clean your aluminum with a stainless steel brush, and remove surface greases with degreasers.
Clamp your aluminum to a backing bar, preferably one made of copper or aluminum. A backing bar will absorb excess heat from the metal, preventing heat from causing the metal to warp.
Preheat the aluminum, to 500 degrees Fahrenheit. Evenly heating the aluminum prior to welding helps to avoid cracking.
Create a welding puddle with the TIG welder, and aim the welding tool at the center of the puddle, to shield the aluminum from the welding heat. Feed the filler metal into the welding puddle, without allowing it to drip.
Avoid gaps between the pieces of aluminum. Gaps can cause warping in the weld, since air cannot absorb heat.