I love it when people share my enthusiasm for wine, and approach it in a humble, willing way. I can't speak for anyone else, but I feel like rehashing how I started in this whole thing, and a few things I've picked up along the way.
First book, the literature that got me intellectually hooked for life - The Wine Bible, by Karen MacNeil. This author is fantastic. An American with New World style, but Old World tastes. Lots of pictures as well!
Lets start off by saying that if you're not willing to spend time and money, then forget about wine. This hobby is all about experience, and experience only comes from tasting. You can read all you want, but it's meaningless if you don't buy and drink wines regularly.
What should you buy though? That's a common question - a lot of people just feel overwhelmed, stepping into a wine store and staring at row upon row of bottles with indecipherable labels. I like my method. I read a bit first, and came upon a region that I really wanted to try. My approach was always Old World - look at wine regions only, as opposed to a specific grape varietal. For example, I knew I wanted to try Rhone wines first, instead of focusing on syrah.
Go out, and buy 4, or 5, or 20 bottles of wine all from one region. Taste them back to back, however long that may take. Tasting wines of a same region together gives you a point of reference, since taste is all relative. It gives you a deeper understanding of the commonalities and differences that a wine region has.
That's it. This is what I'm still doing. Just going from region to region, paying attention to how vintage affects the wine. Supplemented with a copius amount of wine-related magazine/blog/print/newspaper reading. It's simply really. All you need is patience, and a spirit to learn.
Great wine glasses don't hurt either.
Oh, and take detailed tasting notes!