generally, one shifter will adjust the front derailluer (that thingy that moves the chain amongst the gears), and the other shifter will adjust the rear. By default on most bikes with integrated brake levers/shifters, the left shifter controls the front, and the right controls the rear.
With Shimano shifters (on all but the very newest DuraAce racing stuff t-mobile's using), you'll have the main brake lever, and then a smaller lever behind the main lever. On the left shifter, pushing the main brake lever in towards the front wheel will shift to a larger chainring, and pushing the smaller lever inwards will shift to a smaller chainring (front gear). On the right shifter, pushing the main brake lever inwards will shift to a bigger cog (rear gear), which results in you going slower. Pushing the smaller lever on the right shifter will move the rear to a smaller gear, which will let you go faster.
On Campagnolo, there's the main brake lever, a smaller lever behind the main brake lever, and then a thumb lever. The smaller lever behind the main brake lever acts just like the main brake lever on Shimano, and the thumb lever works just like the smaller lever on Shimano (no flames from Campy folks please).
hope this helps some!