This is simple. A basket hanging below the balloon safely holds passengers and also the flame that sends heat into the empty balloor. Heat rises, and so does a hot balloon. Usually gas is used for this.
The size of the flame and intensity of heat determines how high the balloon will fly. The material used for such balloon must obviously be inflammable!
Hot air makes a balloon fly. The air is heated with a propane heater similar to how you might heat your outdoor barbeque grill. The balloon stays afloat because air is a gas and when it is heated, the molecules in the air expand and become less dense or lighter than the air outside the balloon.
A person piloting a hot air balloon can control the rise of the balloon by adding more hot air and the fall of the balloon and the landing by letting the air inside the balloon cool down. The rest of time pilots maneuver horizontally by changing their altitude to ride with the wind, since wind blows in different directions at different altitudes.