Clouds are made up of tiny water or ice droplets, depending on temperature. This implies that cloud density is greater than that of dry air. Why don't clouds sink through their surrounding atmosphere rather than float by in a variety of formations?
The short answer is, it's a colloidal suspension, effectively. See http://www.scientificamerican.com/article.cfm?id=why-do-clouds-float-when
Clouds don't start as clouds. Most of them start out as humid air, typically from evaporation from a large body of water (say, the Pacific or Atlantic ocean, and most of that between latitudes 30 degrees north and south).
Now humid air is LIGHTER (less dense) than normal air. This is because gases like to run the same number of moles (number of molecules) per cubic meter, and an H2O molecule weighs less (much less) than an N2, O2 or CO2 molecule.
So, the humid air rises until is cools at higher elevations, forming clouds. Even at this point, where the microdroplets are denser than the surrounding air, they are not so heavy that they can force their way down. They are trapped, sort of like grains of sand that get picked up in a sandstorm. At some point, though, the micro-drops collect into not-so-micro drops and start falling. As they fall they merge with other moisture and micro-drops to form rain or other precipitation.
To understand how these micro-droplets or micro-crystals can stay up so long, think about hail storms. We know now that larger hail sizes can be attributed to the initial tiny hail dropping for a distance and then being blown back up by thunderstorm updrafts. The tiny hail balls go up and down, up and down; and get coated with a new layer of ice each time, until they are finally heavy enough to overcome the updrafts and fall to the earth. At his point they may be golf ball sized or even larger. Think of it: billions of balls of hail, each the weight of a snowball, being suspended in space by atmospheric conditions. After pondering that, it is not hard to believe that micro-droplets can stay up there.