Obtain the proper filler metal from your local hardware store, or from the Internet. The appropriate filler metal for 3003 aluminum is 4043 aluminum or 1100 aluminum.
Set the TIG welding torch to the proper specifications. Make sure the electrode you are using is either pure or 2 percent ceriated or thoriated tungsten and set the A/C balance knob to around 70.
Fire the welding torch to create a small pool of molten metal on the surface of the 3003 aluminum. Hold the filler metal in the pathway of the heat, so that it melds to the surface of the aluminum.
Use the welding torch to make a a series of small welds over the surface of the 3003 aluminum, until you obtain the welding integrity that you desire.