Wine and cheese -- delicious as they are -- are fairly old news in the food world.
There's an increasing awareness that beer, once upon a time regarded as wine's loud, lowbrow cousin, can match wine's ability to pair with cheeses... or even leave it in the dust.
Beer's flavors tend to complement (rather than contrast) those of cheese.
And beer's secret weapon is its carbonation, which helps to scrub the tongue of sticky cheese, allowing us to taste all the flavors available to us.
Getting started is easy -- begin with your favorite cheese or cheeses, and find beers with notes that are complementary to what you're eating. For example...
Hard Italian cheeses like parmesan and asiago have a nutty characteristic that makes them a natural match for nut brown, Abbey-style, and English ales. Soulful and mellow -- meet soulful and mellow.
Cheddar pairs well with a number of beers -- pale ales are good place to start, with their malt and hop balance and medium body -- they're substantial enough to stand up to cheddar's relatively assertive flavor, but they won't shout it down, either. Belgians with a bit more bourbon-like richness can also complement an old cheddar's restrained zip.
Blue cheese does really well with fruit beers such as Belgian fruit lambics and good pear or apple draft cider. Lagers and ales pair up well, too -- blue's strong personality makes it a particularly fun cheese to experiment with.
Brie and camembert work well with full-bodied, malty Marzen (Oktoberfest) lagers, and with anything that's got a fruit note (like fruit lambics.)
These are just some initial ideas -- sites like the Cheese Cupid will have a lot more. But the best possible thing you can do (maybe ever) is to buy three or four of your favorite cheeses and three or four different styles of your favorite beers... and then just taste. Pair and taste, pair and taste, and pair and taste. If you're serious-minded, take notes on the best matches. Otherwise, just make sure you've got some friends in the house and call it a party.