I ran across this thread as one of the related threads to another one I was reading through.
Obviously there are some folks here who know their stuff, and I'd pay attention. I've learned a more than bit myself just now.
Unlike most of the folks here, I learned how to weld using a gas rig, and I still use it most of the time. I have a Lincoln Pro Mig 135 but it hasn't gotten much use since I bought it several years ago. It just always seems to be easier to grab the gas rig if I have minor work to do.
I have done some gas welding on a frame -- non structural area. A previous owner of my '78 XS had cut the loop off the back of the frame cuz he wanted to build a tracker and thought he needed to get rid of it. Fortunately when I bought the bike from him, I got the loop too and was able to weld it back on. I found that the trick was to use the right size flame point or else I'd blow through the tubing and create a hole. Easy does it. Once I found this happy medium, I was able to reattach the loop with a minimum of fuss.
So I taught myself how to weld with the help of the rather well-known and widely used shop text,
Modern Welding. I have two editions -- one dating from the 60s and the other from the 80s. It is still being published. Very highly recommended:
http://www.amazon.com/Modern-Welding-William-Bowditch/dp/1566379873
The hardcover edition is pretty pricey, the softcover much more affordable, especially if you buy used. I like this book because it is thorough and very easy to understand. It was written for high-school and college vocational classes so its long on practice, but still covers theory well.
Another book on welding I bought was
Performance Welding.
http://www.amazon.com/Performance-Welding-Motorbooks-Workshop-Richard/dp/0760303932
I didn't find it quite as useful as the text, but it was interesting to see the various projects the author has done. I also learned from this book that brazing, when done right, can be a viable substitute to welding, even for structural purposes.
For fabricating or tacking together small parts, a welding table is essential, I feel. I put together a simple one using an old Black and Decker (Shop Task I think it's called?) collapsible utility table, and laid a slab of 2' x 3' x 3/8" steel on top of it. The steel flat was big enough and thick enough (such that it acted as a heat sink) where I was able to use it as a welding surface without having to worry too much about penetration.
For practice, I bought a few pieces of 2" x 1/8" thick stock, a few feet long from my local Home Depot, and cut them up into pieces with my chop saw. Then I proceeded to weld them back together. That's the best way I know of to tell if you're getting good penetration, cuz you can examine both sides of the weld, and even cut it apart to examine it if need be. It was only after I was able to produce a decent bead welding the flats back together that I began working on any welding projects.
This was all gas though. With my MIG welder, all I've done so far is tack stuff together, but if I were to need to do some serious work with it, I'd start first by practicing welding flats back together and then do the same thing with scrap tubing.
Welding isn't rocket science, but it still requires that one pay close attention to detail, use the proper techniques, do conscientious prep work, and that one practice, practice, practice.