It used to be a rule of thumb that fish and chicken go with white wine, and red meat goes with red wine. But there's more crossover now because winemakers have come out with lighter red wines like Pinot Noir that go well with fish and chicken.
Obviously, if it's baked or broiled, you'll want a different wine than a dish with a heavy sauce. A Chardonnay, Sauvignon Blanc or Fumé Blanc will likely go well with lighter dishes.
Stronger-flavored food needs stronger wine. Dry wines generally go well with food, but if you don't like dry wine, go with a semi-sweet wine.
Given the fact that most Americans have grown up drinking sweet sodas, it can take some of us a little while to acquire a taste for dry wines. A good tactic to develop your wine palate might be to start out with sweeter wines and gradually start drinking drier wines. Some of the very sweetest wines include those made from fruits other than grapes, such as apples (hard cider), pears (perry), blackberries, peaches, and cherries.
Wines don't have to be expensive French or Californian to be good. Oregon, Texas, and other states have started to produce some nice wines that are reasonably priced.
Ultimately, when picking out wines, you need to find out what you like, not what somebody says you should like.
The single best way to figure out what you like is to go to a winery where you can taste a number of wines side-by-side. But if going to a winery isn't an option, you can host a wine tasting get-together with friends. Individuals or couples can bring a different bottle of wine to the gathering, thus allowing everyone to try out many different wines at once without any one person having to spend a lot of money.