1. Most meat and dairy contains fat. There are three ways to choose wine to "marry" well with the fat:
a. A wine with higher acid, which balances the fat;
b. A with higher tannin (from oak aging, or from time on the stems and seeds) cuts the fat in the mouth; and
c. A wine with higher alcohol matches the heaviness of the fatty food.
I might add that wine also cuts the fat chemically--just sautee some fatty meat and remove it, leaving some fat and fatty bits in the pan, and then add wine and scrape--the wine breaks up the fat. This is simplistic, but in my mind I visualize the wine's breaking up the fat before it can be deposited in my arteries ;)
2. With an acidic dish, make sure the wine has more acid than the food. This can mean reducing the amount of vinegar in a salad, or looking for higher-acid wines. In a white wine, about 0.70% Titrable Acid (TA) is a good target level to consider; in a red, it's often closer to 0.60%. If acid gets much higher than those target levels, then most wines will need some residual sugar (RS) to balance the high acid. But bear in mind that copious fruit in a wine can fool the tongue into thinking a wine is sweet when it's really dry.
3. Salty foods call for sweet or sparkling wines.
4. Desserts need wines which are sweeter than the dessert.
