EDIT: just want to say, I AM NOT A WELDER!!!!! but have done alot of reading and this is just the tip of the iceberg. I've welded a couple of things for my bike, but nothing structural.
PROCEED WITH CAUTION!
You can watch alot of videos, but welding is an perhaps more so an art than it is a science. It takes practice and a lot of it.
If you really want to DIY:
Stick to carbon steel at first. Stainless is difficult and aluminum is VERY difficult.
Make sure you have the proper safety gear!!!!!!!!!! Harbor Freight has a good auto darkening helmet for about $50 or $60
Gloves, long sleeve shirt, and jeans are a must!
Go MIG/GMAW(these terms are explained in the links below)
Skip the flux core welder.
Go for a gas welder. this will have a higher cost, but the results will be much better.
whatever you're welding, the Miller website has a suggested gas/voltage/wire gauge/wire feed settings.
http://www.millerwelds.com/resources/calculators/mig_solid_amperage_calculator.php
a good 110V machine will do what you need.
Stick to a NAME brand welder. there are about 5 or 6 reliable brands with parts/service support. That bargain welder might not be a bargain when it malfunctions and you can't find parts or someone willing to repair it.
a bunch of youtube vids.
There's a ton of info here.
http://www.customfighters.com/forums/showthread.php?t=27005
Before doing anything that you're going to be trusting with your life, plenty of practice and do some destruction tests to see how well your welds hold.
Learn about triangulation of structures and look at some pics of other homebrew subframes.
there are welding forums galore and there is a "heavy metal" forum here if you have any questions.