In college what we drank was jug wine, Sangria, sloe gin fizzes, and the occasional 100% grain alcohol that the pre-med guy would get from the lab. Taste wasn't exactly the idea. For many years, we didn't exactly drink much in the way of any wine at all. Then we were introduced to "good" wine. This wasn't something that you just drank, it was another facet of the meal, food to be enjoyed just like the entree or dessert.
About this time a local "fancy" market started doing "winemaker dinners." This being California, there was no lack of some of the best people in the state showing up. The market was trying to get business, so it was inexpensive and the 5-course meals were great. And so was a lot of the wine. While it was interesting to listen to the stories the winemakers, cellarmasters and producers would tell (and try to decipher some of the questions that the knowledgeable folk asked), the most important part was that this was a way to be introduced to a lot of different wines, alone, and with food.
Dri, who has the memory between us, could remember what was good, or what she or I liked, and still can to this day. I'm a lot slower and my test (I thought I'd invented it, but then saw it in a magazine--later) was the "GDE" test. Did it "go down easy?" Matching wines was Dri's job and I knew I liked what I drank. I also started to know what I didn't like. Dri and I don't always agree. Neither will you.
We bought a few books and started to visit wineries, mostly in California, some in Washington and Oregon. We went on the tours, some of which were big and crowded. As we gathered up our nerve about us, we found that we could make appointments at little wineries which would show just the two of us around (often it would be the owner/winemaker doing the tour), talk to us for hours about their operation and about wine, and let us taste some of the "good stuff." (Word of mouth is always good advertising.) It also turned out that some "big" wineries will do the same, just for the asking. After a while one tour looks like another, but we just like being in the usually cool winery and drinking in the scents of grape and wine and wood that jump out at you--and learning about the winemaker/owners. Even when there is no tour, many small wineries will, on appointment, let you taste. (Please, don't be pushy with them. They're doing you a favor, too. They have a business to run and lives to live. We always ask if they have time and when is best for them!)
We didn't try to hit every place in Napa, we slowly picked a few places that we thought had good wine, and went and spent time. And bought some to keep.
So now we drink more wine and we're still learning. We found, as most will tell you, that the best way to learn about wine is to drink it. So true. Lectures, books, magazines, this guide, other people, etc., will help you and maybe get you started along the right track. But what they have to say are just clues to the easily solved puzzle of what you will like.
Two interesting learning tools: restaurants that serve fine wines by the glass or have multi-course fixed price meals serving different wines for each course and wine tastings (often of verticals that will let you see just how a wine ages and when it is young, ready, or too old all at one sitting). Many restaurants have wine tastings as do wine clubs and associations.
You can also do your own wine tastings (everybody brings a bottle of something, perhaps all reds, or all one varietal, etc.). Perhaps you host and have the guests chip in on the costs. This way you avoid duplication of bottles.
Read Kevin Zraly's "Windows on the World Wine Course", a very easy to read book with lots of graphics.
Take a wine appreciation class. These can usually be found through university extension, junior/community colleges or even large wine shops. These will introduce you to terminology, basic wine types, how to evaluate wines, etc.
Find a tasting group, or a good wine shop that puts on tastings, preferably both. It is prohibitively expensive to taste a lot of wines if you have to buy a full bottle for each wine. Typically, a good wine shop should be able to point you to a few good tasting groups. There's used to be a "Les Amis Du Vin" chapter in most major cities, but I'm told the national organization has disappeared. A new organization called "Wine Lovers International" is trying to incorporate as many of the old Les Amis chapters as it can. Get copies of wine tasting newsletters, and try several wines recommended by each of them to see which ones most closely match your palate, then subscribe to the most appropriate ones. There's a listing of these resources elsewhere in this document.
If all else fails, get some friends together (who at least enjoy wines--and maybe even if they don't) for wine tastings. It's also not a bad idea to make friends with people who have cellars full of wine (!).
An important thing to do for any person who wants to start drinking better wine, is to find one or two wine merchants that you like, and to become recognized as a loyal customer, even if you don't initially spend a great deal. See which shops have tastings open to their customers. Tell the proprietor about your interests, taste, and budget. Many wine shop owners are enthusiasts who love to help (and talk) about wine. Try the offered wines then decide whether the wine is as the proprietor described it? Is it about what you asked for? If so, go back for more. A good merchant will repay your loyalty (and you'll repay theirs, and so on . . . )