Clouds float because they possess less density than the air around them. Clouds are composed of tiny water droplets and ice crystals that are only a few microns in radius, too small to develop any appreciable fall velocity.
Clouds are composed of atmospheric moisture that has evaporated from the liquid state found on the surface of the planet to a vapor that is carried upwards by air currents. When it reaches the colder temperatures found in the upper atmosphere, water vapor begins to condense into tiny droplets and ice crystals which form clouds. While the largest cumulonimbus clouds may weight several hundred tons, they are able to float because they possess less density than the air below.
The upwards vertical motion of wind gusts and currents also contributes to the floating appearance of clouds. As drops and ice crystals begin to condense and collide, their larger mass may allow them to develop the vertical velocity needed to fall back to earth as precipitation. The fall velocity of larger droplets and crystals can be offset by the force of air that is moving upwards. These rising air currents continue to expand as they encounters the decreasing air pressure of the upper atmosphere, a process that aids in cloud growth and formation.