There are probably infinite shapes which clouds can form, given all the variables in the atmosphere, but three basic shapes are used to classify clouds.
Cumulus clouds are the flat-bottomed, tall clouds that look like whipped cream or cauliflower.
Thick layers of clouds, like blankets in the sky, are called stratus clouds.
Cirrus clouds tend to be high in the air, small, thin, and wispy.
Clouds can exhibit characteristics of more than one type, and more than one kind of cloud can be in the sky at any time. When clouds have combined traits, their names are generally made up by joining the names of the different clouds.
For instance, cirrostratus clouds have the height of cirrus clouds and something of the shape of stratus clouds.
Clouds likely to precipitate are called nimbus, as in cumulonimbus (cumulus rain-snow clouds) or stratonimbus (stratus rain-snow clouds). Cirrus clouds are frequently too thin to accumulate enough condensation to cause precipitation.
The three main types of clouds are cirrus, cumulus, and stratus. Clouds can be combinations or variations on these three types. Nimbus or Nimbo signals likely precipitation. Alto means high.
Clouds below —100° Fahrenheit (-73° Celsius) are completely ice.