Hot air balloons are based on a very basic scientific principle: warmer air rises in cooler air. Essentially, hot air is lighter than cool air, because it has less mass per unit of volume. A cubic foot of air weighs roughly 28 grams (about an ounce). If you heat that air by 100 degrees F, it weighs about 7 grams less. Therefore, each cubic foot of air contained in a hot air balloon can lift about 7 grams. That's not much, and this is why hot air balloons are so huge -- to lift 1,000 pounds, you need about 65,000 cubic feet of hot air! To find out exactly how this works, skip to Air Pressure + Gravity = Buoyancy.
To keep the balloon rising, you need a way to reheat the air. Hot air balloons do this with a burner positioned under an open balloon envelope. As the air in the balloon cools, the pilot can reheat it by firing the burner.
Modern hot air balloons heat the air by burning propane, the same substance commonly used in outdoor cooking grills. The propane is stored in compressed liquid form, in lightweight cylinders positioned in the balloon basket. The intake hose runs down to the bottom of the cylinder, so it can draw the liquid out.
