The balloons need to be quite large because this upward force is quite weak, a fraction of an ounce per cubic foot of air. But if you make the balloon large enough (many balloons are 90,000 cubic feet) the buoyant force can be great enough to lift the balloon (800 lbs) and its passengers.
We also showed an equation that can give, approximately, the amount of lift to expect from heating the air a certain number of degrees.
For additional info:
Wikipedia entry on hot air balloons
A nice explanation of the math and physics involved with balloons at How Stuff Works