I would start out by reading about welding on Wikipedia. If you can set out to learn about the 3 main types (arc, MIG, TIG) on Wikipedia, and get that information firmly into your head, you'll have a good basic knowledge of some of the general concepts. After that, then hit Youtube and find the welding 'how to' videos to see some weldors in action.
If you like to read (offline) I reccomend "Welder's Handbook" by Richard Finch for a good source of introductory information. Welding for Dummies is also a good source for a beginner. I would actually get the Dummies book first, if you're only going to get one book.
After that, you might look for local welding classes. While it's common to find multi-week or month classes, you might be better to try to find a 1/2 or 1 day introductory class that will let you get a bit of hands on time with the equipment and actually try welding without getting into the commitment of a long and expensive class. If you live in or near a large city, you might see if there is a company that does casual learning classes (instead of trade school-like classes)
If you're still interested, then you'll probably want to get your own welder. I won't go into what welder to buy, but keep in mind that the kind of welder you buy depends on the kind of welding you need to do (or want to do). This basically boils down to the materials, objects, and circumstances of your welding. The only thing I will add is that the really low-cost generic-name welders can pose a problem for a novice because they can make it difficult to get clean and strong welds if you don't already have good experience.
Keep in mind that although it's called 'welding', it's more realistic to just refer to the concept of 'metalworking'. It's not practical to just do welding; you also need the ability to cut and form metal, and you need other tools to do that. The welding machine is just a tool to join metal. So don't think you can pick up a cheap welder for $250 and be good to go. You may also need a grinder with abrasive cutting wheels and grinding wheels, possibly a cutoff saw, clamps, magnets, and more. You'll also need a good welding helmet and gloves. To make the best welds (with a MIG or TIG welder) you need shielding gas which is cheap, but comes in a gas cylinder that is not cheap. At that point, your $500 MIG welder has just turned into an $800 deal with all of the accessories you need.
After that, you need to practice, practice, practice.
Oh, you asked about links. Go over to the forums at www.weldingweb.com
and hang out there.