Starting from the lighter end of the spectrum are your pilsners and lagers. I find these work better with seafood, as the taste is lighter and won't overpower the flavor of the food. In New Orleans, a boiled crawfish is best washed down with a light pilsner from any of the megabreweries.
Moving along on the beer styles, we come to your pale ales and ambers. As these are a little heartier, they can be paired with similar food. Try having Chicken and Pork dishes with ambers for a great match up.
Next we come to the so called "dark side of the beer". I refer to stouts and porters when I refer to dark beer. These are among the heaviest regarding taste and alcohol, so you can pair them up with the heartiest foods like steaks, ribs, and similar dishes.
Beyond those basic distinctions of beer are some specialties like barley wines. Barley Wines are higher in alcohol content and in my honest opinion don't really match up with any food in particular. The alcohol is just too strong to blend - imagine eating food with straight vodka. Does that sound like a good idea to you?
The key to deciding on which beer to pair with your food is to find a combination where the overall flavor is not overpowered by any one item. A little prior planning can give you a pleasant meal.