According to Eric Asimov, wine writer for the New York Times, the best place to learn about wine may be your own home. Eric suggests that the best way to learn about wine is to do some "systematic wine drinking" at home.
Eric's advice is to tell your local wine retailer that you are interested in learning about wine and ask them to recommend twelve different wines that are worth getting to know. Preferably, the recommendations will include different styles and grapes from around the world. Be sure to set a price limit you are comfortable with. Eric used a $250 budget. Since a case is 12 bottles, that's about $20 or so per bottle. You may prefer to spend $15 a bottle.
Eric's advice is that you open a bottle every other night or so and take notes on what you like about the wine, what you don't, what you ate with it. Then, when you have finished your case, take your notes back to your wine retailer and ask them to recommend a second case based upon what you liked in the first one.
You can read more of Eric's thoughts about systematic wine drinking at home here and here.