How do most American brewers carbonate their beer?
The big breweries (Bud, Miller, Coors, Sam Adams) all filter their beer, this takes out any remaining yeast. Then they force carb the beer before they pasteurize it (killing any remaining bacteria or yeast). Some of the smaller craft and micro breweries still bottle prime, where they add a small amount of sugar to the brew before bottling. This is referred to as bottle conditioning, and will cause fermentation to start back up slightly, and that is how the beer gets carbonated. These beers will have a small amount of sediment in the bottom of the bottle, which is the leftover yeast after bottle conditioning.
