In order for air to lift a balloon, it must be hotter than the surrounding atmosphere. The original Montgolfier balloon was a hot-air type. When the brothers observed a piece of ash rising from a fire, they correctly deduced that the ash was being carried upward by the warm air from the fire.
Today, hot-air balloons use propane burners under an envelope to heat the air inside the balloon to more than 150 degrees Fahrenheit. Regulating the burners allows the balloon to rise, float with the air currents, and then descend as the hot air cools or is vented.
Hydrogen is a very volatile element, and the lightest substance in the universe. Hydrogen production involves electrically separating the elements that comprise water to produce free hydrogen and oxygen. The hydrogen then rises above the oxygen, and collects in a separate container.
Although hydrogen fires have produced many spectacular ballooning accidents over the centuries, the gas is used today not only for free balloons, but also for disposable weather balloons. Because hydrogen is not flammable unless it's contaminated with air, balloonists take great care to keep the hydrogen in their vessels pure during inflation and flight.
Hydrogen is relatively inexpensive, so it's easy to replace when vented. When a hydrogen balloonist wants to descend, she valves away the hydrogen and the balloon loses lift. When the balloon lands, the balloonist opens a large rip panel and all the hydrogen escapes.
Today, all manned airships (blimps) and most free balloons use helium. Helium is an expensive lifting gas compared to hydrogen, because it's not as plentiful. However, it has the advantage of being completely inert; it will not burn, nor will it corrode any other material.
The United States Navy began flying blimps filled with helium in the 1920s; since then, all airships in the United States have flown exclusively with helium. The cost of helium represents a significant portion of the expense for airship operations. For this reason, airship operators avoid venting the gas as much as possible.
