Unless you live next to a tall skyscraper or a mountain, it is not possible to figure out the height of a cloud just by looking. This is because there are no points of reference in the sky. That's why our determination of height relies on identifying the cloud type.

Hints for cumulus-type clouds:
º Low cumulus cloud cells (the individual puffs of cloud) are about the size of your fist or larger, when you hold up your hand at arms' length.

º When cumulus clouds are just forming or evaporating, they can look considerably different from those that are fully-formed. Do not be fooled! Sometimes you can tell that the clouds are forming or evaporating if there is strong wind and both new and fully-formed clouds are moving along in the same layer. Other times you may have to look for other clues.

º Mid-level cumulus cloud cells (altocumulus) are about the size of your thumbnail when you hold your hand at arm's length.

º High-level cumulus cloud cells (cirrocumulus) are about the size of the nail on your littlest finger - again, at arm's length.

Hints for stratus-type clouds:
Without the size clues provided by individual cumulus clouds, determining the height of stratus-type clouds can be a challenge.

º If it rained recently or is about to rain, you are most likely dealing with a low-level stratus cloud. While it is possible for rain to fall from mid-level clouds, it is quite rare.

º If it is raining during your observation, you have nimbostratus (or cumulonimbus - but the difference should be obvious! The latter is a thunderstorm). The terms nimbo/nimbus are from a Latin word for rain.

º If a stratus cloud is so thick you can't even figure out where the sun is, most likely it is a low level stratus. The visual opacity of such a cloud is opaque.

º If you can see the sun but it looks diffused (like looking through a glass bottle), most likely you have altostratus. The visual opacity would be translucent.

High-level cirrostratus will generally be thin enough that the sun is still quite distinct. If the cirrostratus is not between you and the sun, you may be able to distinguish cirrostratus as being so thin that parts of the cloud appear bluish (that is, you are seeing through to blue sky). The visual opacity is transparent.

From: NASA - Lin's Tips for Cloud Observers

The Cloud Appreciation Society has lots of resources - books, posters and an app - to help you learn more about clouds.

Check them out here