Prepare soil by mixing equal parts of potting soil and sand or perlite, or use special cacti and succulent potting soil sold at most nurseries.
Choose a pot that is half as wide as the height of the succulent you wish to plant. Clay pots are a popular choice, but plastic pots conserve water and weigh less so they're easier to move around. Bonsai pots also work well for fibrous-rooted succulents that don't need the depth of a taller pot. Use taller pots for tuberous succulents with tap roots that require more depth.
Place a few shards of broken clay pot or some small pebbles on the bottom of the pot to cover the hole. You want to allow water to drain from the bottom of the pot, but don't want the soil to fall out.
Fill the pot with the soil mixture until it is about one to two inches from the top.
Snip a cutting from a larger plant, such as a pup. A pup is a smaller version of the larger plant that grows on the larger plant . There is a small pup in the bottom middle of the photo, with slightly larger pups on either side. Some pups will have a stem attached, others just grow out of the larger plant without a stem. Snip as close to the root of the stem as possible. For pups without stems, you can gently grasp the pup and pull it off the larger plant, it will sprout roots.
Dig a shallow hole just deep enough to cover the roots, but not the leaves. Place the cutting into the hole and cover the roots.
If you're planting a succulent from a nursery, loosen it from its pot, loosen the dirt around the roots, and snip off any damaged roots, before planting as above.
Succulents like a lot of bright light, but not direct sunlight. If indoors, a southern facing window is best.
Wait about a week to water newly planted succulents, and then only dampen the first time. Very young succulents, however, may be watered right away. The key for both young and old is not to over water.
Succulents require very little water. You may even want to wait until the leaves begin to pucker a little before your next watering.
In the summer, give your succulents a good soaking once a week. In the winter, increase to two or more weeks, and make sure you let them dry out between waterings.