I'll take a little different perspective. If you are getting 'into' wine, then you want to drink what you like, but knowing something about varietals, styles, etc. can help you pick wines you're more likely to enjoy.
I know it sounds weird at first the way wines are described, but the more you drink decent wine, the more the terms make 'taste sense.' Since most of taste is actually smell, that's why you swirl it in the glass and smell a wine before you taste it.
All wines split into dry vs. sweet; very dry wines can be called things like flinty, tannic, and undesirable is astringent. Sweet can be called anything from soft to fruity to syrupy.
In whites, Chardonnay is the wine that tends to develop the most complexity and can have real backbone, so it tends to run to higher prices at the top end. You can get very nice chards for $8-12, and sometimes less. There are 'big buttery' chards, and 'fresh, citrusy' ones and every possible in between. Now it helps me to know that I hate a 'grapefruit' or 'lemony' finish (final taste) and I love 'buttery' or 'caramel.' Some people are the reverse, purely a matter of taste.
Here's a description of my favorite Chard: Complex aromas and flavors of ripe pears, honeysuckle, apricot and spices opening together on the palate with generous but well-integrated oak, nutmeg, and minerals, and a very long, creamy finish with a hint of hazelnuts. (The oak and minerals lets you know it's dry and clean and has some power to it despite all the rich flavors.)
Other whites to try are chenin blanc, voignier, pinot grigio, sauvignon blanc. The first two tend to be softer and a bit fruitier, the last two more fresh and citrusy. I had a wonderful Spanish white from AJ's lately, $12, an unfamiliar grape that started lightly citrusy but got more buttery by the aftertaste, but I can't recall what it was. It was a perfect summer evening white wine.
In Reds, Cabernet Sauvignon is the great grape -- it can produce wines that last a hundred years or more before they lose their quality, and a great Cabernet (and I have been lucky enough to have rich friends and have tasted a few) is an amazing wine experience. It might start by grabbing your tongue and ringing it like a church bell, then immediately open up into intense plum and dark chocolate flavors, while the aroma may add a little bit of tobacco, leather, and raspberries. Then it develops undertones of black currant and a hint of oak (along with the plum-chocolate), which roll together to produce a rich harmony that seems to go layer on layer, before slowly melting away into a velvety, burnt-sugar and raspberry aftertaste. Sorry, got carried away...
Zinfandel is a less complicated, but even bigger red, often jammy (imagine condensed blackberry jam without the sweetness) and peppery and can be like a head-on car crash; I love a monster Zin. Merlot is sort of the tuxedo-clad but simple-minded cousin of Cabernet, and while they can be very nice, I think merlots are more prone to off-flavors like cooked green beans or green peppers. Pinot Noir is a very complex, lighter red, often described as cherry, strawberry, violets, etc. It is the French red grape. I have had magnificently flavorful pinots now and then, but they are expensive and if they fall short, I think they are dull.
Vintages do matter. In a great year, the weather lets the grapes produce the exact balance of natural sugars and color and so on at the right density. Too wet, and the grapes actually are more watery and thin wine may result, too dry or too hot and you get other problems, and of course the weather right at harvest time is critical. So if you know a certain year is very good for California, or for Australia, or wherever, you can guesstimate that many 'average' price wines will be of above-average quality regardless of brand. In a really bad vintage year, you know the really good wine is the exception to the rule.
Brands and where a wine is from can also help you guess more wisely, because brands = winemaker, and each winemaker has a certain style he or she aims for if the grapes allow. Some brands are known to almost always produce a very respectable wine. Thus I think Bogle almost always makes a nice Chard, Zinfandel, and Petite Syrah, although their Cabernet can be iffy.
Countries or regions tend to have certain styles -- Australian wines seem to be 'big' rather than subtle, lots of flavor and in your face. There are many reliable Australian brands for red or white. Chile produces some knockout reds -- often rich, dark, powerful -- try 'Roots' Cabernet. French red and white wines tend to emphasize floral aroma, complexity and subtlety, and frankly, I often find them a bit thin for the price until you hit mid-to-upper range. Italian reds are big, very dry, dark, and in my price range, they tend to be overly tannic and hot. German whites are on the fruity, soft side, but some complexity.
Pacific NW whites are generally smooth, balanced, a little softer and fruitier, but refreshing. California whites - Chards normally go for sophistication and complexity. The other whites generally aim to show their varietal quality -- so Sauvignon Blancs are fresh, bright, acidic, citrusy, Voigniers are buttery, fruity, and 'round.'
California reds - Cabernet is the king, best from Napa or Sonoma and again they go for complexity, intensity, and structure. Pinot Noir tends to be more the Pacific Northwest, or try Santa Barbara. Sonoma Zinfandels are often big fellas.
I'd suggest looking at a couple of Wine Spectator magazines, in their ratings section, and pick maybe two or three whites and two or three reds that are reasonably priced and well-rated, and with very different descriptions. Have some friends over, and do a little tasting. See if you can identify some of the flavors and aromas -- it takes practice. (Remember to keep plain bread and water around for nibbling between tastes of different wines -- then introduce a couple different types of food and see how food and wine do and don't work together.)
NOW you're ready for wine-bar tastings.