Hot air balloons were first invented by a Chinese general named Kongming around 220 AD. Kongming’s lights were small oil lamps inside a paper bag. By 1200 AD, they were popular at festivals and had been used by the military as banners and signals.
The first passenger flights occurred in France in 1783. The Montgolfier brothers worked at a paper mill and were able to get a paper bag (balon) to float by holding its opening over a fire. They worked to improve the design and their first passengers were a sheep, rooster, and duck. Two months later a balloon successfully carried three humans.
Hot air balloons float because when heat is applied to air, it increases the movement of air particles, which causes them to move farther apart. The movement of the particles maintains the air pressure, but decreases the density (and weight) of the air. Cooler, heavier air pushes the lighter air toward the path of least resistance, which is upward. Check this NASA site for an explanation and some activities. You can also search for “Archimedes” and ”buoyancy” in your favorite browser for a lot more.
Visit HowStuffWorks for a great overview of hot air balloons and how they work.