IANAW (I am not a welder).
You could probably teach yourself the theory, and memorize the different techniques and the best practices on your own, but since actually doing stuff constitutes half your education anyway, it’s probably not enough. Considering that welding can be pretty dangerous, I would probably recommend that you call up your local community college or technical school and see what they have open. The armed services would probably also teach you if you were willing to enlist.
I am a welding engineer.
And despite my education in all of this, I have no idea how to physically weld well. I’ve never actually had to it. I’ve considered taking community college classes myself, because even knowing all of the science, I’d want to practice in a controlled environment.
(In my industry, most of what we do is resistance, drawn arc, or laser welding anyway, and the GMAW applications are all robotic.)
Keep in mind there’s (at least) two kinds of welding.
-Welding that isn’t all that critical (go kart frame…heck, even welding up parts of the trailer doesn’t qualify as critical)
-Welding that is. (Think NASA, Roll Bars, Rollercoasters)
Great post/username combo!
Fourth time this year… I’m on a Roll! 
You might check out art studios and similar places for welding classes. I know of at least one place each in the Bay area and in Boston that give welding classes (including women-only ones).
I am just finishing up a 17-week welding class at the local community college. It covered SMAW (stick welding), GMAW (Mig or Mag), GTAW (Tig), FCAW (Flux-cored arc-welding) and oxyfuel welding and cutting. Of all of those, I would pick GMAW as the one that would be the easiest to learn by yourself. The others require more equipment knowledge and training. Mig is just pretty much pull the trigger and go. The downside to Mig is that if you’re using it in short-circuit mode (the most common), you should not be using it for anything structural, as it is notorious for lack of fusion (resulting in potential failure of weld). And you should we very familiar with the various safety issues before you begin.
By the way, the welding class has been awesome. Easily the most enjoyable and most satisfying college level class I’ve taken. I highly recommend it.
Oh, and get an auto-darkening welding helmet. Otherwise you can’t see at all until you strike an arc, and not well even then. It’s hard to weld when you can’t see what you’re doing!
Voltage doesn’t kill, Current does.
If the voltage isn’t high enough the current won’t pass through you.
This. Note that it is possible to weld metal with a 12-volt car battery, which can supply hundreds of amps - and yet you can safely grab both terminals with your hands, since the 12 volts isn’t enough to move any significant current through your body.
I’m going to stick with what I said, current kills. There are associated risks with electrical shock injury and welding and I think that if someone is just learning they should be aware of these.
I had a friend that blew a hole in his elbow welding a floor panel in a car using a mig welder.
I do not suggest there are no electrical hazards associated with welding - only that “voltage doesn’t kill, current does” is not a particularly helpful statement to to make with regard to electrical safety.
While welding can be hazardous, I would venture to say that a circular (skil) saw is a much more dangerous tool (and a router might even be more dangerous). Just use some common sense, and you’ll be fine.
Here’s the thing. Electricity makes sence…until it doesn’t, or you have less than 100% grasp of the situation.
You can work on a live circuit, 110v, light switch. You take care to use one hand, and make sure your body doesn’t produce a path-to-ground through your heart, and you have good insulated shoes. Heck, a little 'ol 100v AC shock isn’t really even that bad.
Until just enough of it finds a path in a way it’s ‘not supposed to’. (say your shoes are damp, or you stepped on a nail that didn’t even break all the way through your sole.)
Then you’re dead, or in serious need of defibrillation.
100 mA can kill a healthy person, if it can find the appropriate route to ground. Your welder is plugged into at least a 20 Amp circuit.
You wanna do the math and come out wrong?
By the same token, a Range is plugged into a 50A circuit, so does that make it inherently dangerous? As has been pointed out above, most welders use transformers to create low voltage at high current. Although there are safety issues, they are not as dangerous as other common tools. A woodworker friend of mine once said that the common router was the most dangerous tool in his shop - because it had an exposed blade (bit) and needed to be set down with the bit pointing up.
I suspect that the most dangerous tool in my shop is my Plasma cutter - it uses high voltage, high current, creates temperatures hotter than the surface of the Sun, produces UV and hot sparks and toxic fumes, uses compressed air, and is deceptively simple to use…
Recently I spent a month as a day laborer. It was harder and duller work than I’m used to, but one must do what one must do…
I saw that the bulldozer drivers had an easier time and were getting paid almost twice what I was getting paid. I heard similar sentiments expressed by co-workers with welding experience, about welding.
Since I now know I’m willing and able to get down and do “dirty work” when necessary, I sometimes wonder whether I should go try to get certified to drive dozers or do welding or something in case I need to enter that labor force again someday. I haven’t really looked into this, though. How much does it cost? What’s the time commitment? How often do you have to renew? Will possible employers (including temp employers) see that I have cert but no work-experience and laugh me off?
I HIGHLY suggest reading this link: http://makezine.com/extras/87.html
It’s not directly relevant to welding, but it might instill a little respect in electricity.
Does the Range have a hazardous voltage differential exposed where you can touch it?
I’m not saying don’t DO it, I’m saying that ‘ignorance is bliss’ is probably not the best way forward.
Death is not always the only bad thing with electric shock injuries, it can sometimes lead to alot of other problems if you survive.
OK, got it: voltage doesn’t kill, current does, except when it doesn’t, and then it can still injure you.
By now I expect the OP has grasped the idea that welding presents electrical hazards, some of them in common with other electrical devices (e.g. hazardous voltages present inside the cabinet when plugged in), and some of them unique to welding (possible high voltages present at the electrode or on the part when welding). Other (non-electrical) hazards are present as well.
Said hazards can be managed, as indicated by the relative longevity of most professional and amateur welders. OP is further advised that best results (in terms of weld quality and operator safety) will be obtained with professional instruction, but adequate results (for an amateur welder) can probably be obtained at a lesser expense by purchasing and reading a suitable book.
This is the book I have. I haven’t compared it to others, but my gut feeling is that it’s not bad.