Clean the aluminum with a stainless steel brush, to remove surface debris.
Clamp the aluminum to a backing bar, made of copper or aluminum. The backing bar will absorb excess heat from the aluminum, reducing the heat affected zone.
Preheat the aluminum, in an oven, to 350 degrees Fahrenheit. This will make it easier to weld thick aluminum, and, in the case of thinner pieces, reduce the likelihood of cracking.
Fit the parts together tightly, and clamp them, if necessary.
Set the welding machine to use 1 amp of current for each 0.001 inch of aluminum thickness. The amount of current affects the diameter of the electrode, as well. Although you should refer to specific directives given by the manufacturer of your welding tool, tungsten that is 1/16 inch in diameter is ideal for 30 to 80 amps of current, while 3/32" diameter electrodes work well with 60 to 130 amps of current and 1/8" diameter electrodes work with electrodes that are 100 to 180 amps.
Strike the tungsten electrode against the aluminum, forming an arc. Instantly pull the tungsten away, without breaking the arc, and hold the arc in place, allowing a welding puddle to form. Over the course of the welding procedure, do not allow the tungsten to touch the aluminum. If it does touch the aluminum, remove the tungsten (while wearing thick gloves), hit the contaminated part against a hard surface, allow the contaminated part to snap off, and reinstall the electrode.
Weld the aluminum in small, regularly spaced intervals. Create one set of small welds at regular distances from each other, then create more welds at regular intervals from the first set until you obtain the welding strength that you desire.