Frankly the main rule to remember when pairing food with wine is that one should drink whichever wine one likes with particular food. Having said that there are some basic guidelines to maximize your enjoyment:
DrinkWine.com lists 5 basic rules:
Match the weight & texture of the food to the weight & texture of the wine
Example: A light-bodied fish like sole works best with a light-bodied white wine like pinot grigio, while a heavier-bodied fish like salmon calls for a richer, fuller-bodied white like chardonnay.
Balance the intensity of flavors in the food and wine
Example: A mildly flavored food like roast turkey pairs well with light-bodied white and red wines like sauvignon blanc and Beaujolais, but in the context of a Thanksgiving dinner featuring stuffing, cranberry sauce, and other strongly flavored side dishes, an intensely flavored white like gewürztraminer or a rich, fruity red like syrah or zinfandel would be preferable.
The five basic tastes are sweet, sour, salt, bitter and umami (the recently discovered fifth taste found in savory foods like mushrooms, tomatoes, soy sauce, and aged cheeses and meats). Salty and sour tastes in food make wines taste milder (fruitier and less acidic), while sweet and savory (umami) tastes make wines taste stronger (drier and more astringent).
Example: A simple cut of beef tames the tannins and brings out the fruit of a young cabernet sauvignon, but chocolate (which some people enjoy with cabernet) will accentuate its tannins and diminish its fruit. Seasonings, such as salt, lemon, vinegar, and mustard, can be used to achieve balance in food-wine pairings, either to make the wine taste milder (salt, lemon, vinegar) or stronger (sugar or umami ingredients).
Flavors are combinations of tastes and aromas, and there are an infinite number of them. You can fine-tune food and wine pairings by matching flavors in the food and the wine.
Example: Roast duck in a plum sauce is well-served by red wines, like barbera or syrah, with pronounced black plum flavors while grilled steak in a pepper sauce will go beautifully with a peppery zinfandel.
Sometimes, the best choice is to counterpoint flavors rather than matching them.
Example: Pairing a spicy dish like Jamaican Jerk Chicken with a high-alcohol red wine may seem logical, but, in fact, the heat in the dish will ignite the alcohol in the wine to produce an unpleasantly hot, harsh impression. A better choice is a low-alcohol, fruity wine like riesling or gewürztraminer, which will both frame and tame the spicy flavors of the dish.
Enjoy your pairings, gentle reader, enjoy!