I can't speak with any authority, as everything I know about gas welding has only been in my head for about 72 hours. That said, I'll tell you what I learned from those that know more than I do.
First, I would recommend finding a competent instructor with experience welding aircraft. You're going to fly in this thing, so you might as well do it right. The EAA SportAir Workshop was great, though they seem to occur somewhat infrequently and are in high demand. If that doesn't work out, an EAA Technical Counselor may be able to point you to a local instructor or community college program. Worth a shot.
Second, you'll need some reference material whether you teach yourself or learn by other means. This EAA book/DVD combo looks good. I have the book but not the DVD.
Finally, you need the equipment. You're going to need a torch, tips, hose, regulators, tanks, and eye protection at a minimum. I was able to try two torches this weekend - a Harris torch, probably this one, and a Meco Midget. The experienced welders seemed to favor the Meco for its fine control and light weight. Other options include Smith and Henrob. I'm probably going to purchase a Meco Midget with a lightweight hose. The Harris torch with the bigger hose can be cumbersome in tight spaces. Regulators and tanks are still a mystery to me as I haven't done much research on that yet. From what people have told me, the largest expense is going to be the tank/regulator combination, which I'm guessing will be more than $100, but less than $500. Goggles or a face shield with a #5 shade should be inexpensive.
That's all I've got for now...