Most of this information comes from personal experience and information told to me by family. I did google some things to confirm the information, so those sources are listed at the bottom.
Wikipedia defines succulents as plants with thickened sections, generally to store water. Examples include jade plants, aloe vera, and hens and chicks.
Caring for Succulents
Keep in mind that succulents vary quite a lot, so all of this information is just general advice. It's always a good idea to research the particular type of succulent you own to make sure you care for it correctly.
Succulents don't have to be watered often. Personally, I water most of mine about every two weeks - less in the winter, since they don't grow much in colder months. I water my smaller succulents more often, since they're in small pots, so the soil dries out more quickly. This depends on the type, of course: I water my barrel cactus about half as often as I water my aloe vera.
It's important to make sure you don't overwater your succulent. Overwatering can lead to root rot, which is difficult to treat and can kill your plant. As a general rule, if you can stick your finger in the soil and the dirt is dry a few inches down, it's time to rewater your plant.
Making sure the succulent has decent drainage is helpful in preventing root rot. Cactus soil is provided at many gardening shops, which will help let any extra water run through the dirt. Terracotta pots (made with unglazed clay) draw excess moisture out of the soil. Making sure the pot has at least one hole in the bottom is recommended, and I personally like to put a layer of pebbles at the bottom of the pot to make sure water doesn't gather below the roots of the plant.
This may seem like a strange addition to some, but coffee grounds are added to the soil of a lot of plants, and can be good for them! However, I've always been told that since most succulents don't do well in acidic soil, this isn't a good idea for them. I googled it to confirm this, and it turns out I wasn't quite correct: according to TheGardenLady, some succulents would be perfectly fine with coffee grounds in the soil, but since most do better in dirt with a neutral pH, it's not a good idea to add coffee ground unless you know that it's fine for the particular type you have.
Believe it or not, succulents can actually get sunburnt! They do need a decent amount of light, though, so I like to put mine by a window. The glass filters the sunlight and prevents burning, but they get plenty of light.
Some succulents are more sensitive than others, though; some of my succulents are farther from the window because they got a bit burnt when they were right next to it. Keep an eye on your plant and how it's reacting to the the lightsource it's provided.
If you live in a place that gets cold, it's a good idea to have your succulents inside, or at least have a way to transport them indoors during colder months. Since succulents have such a high water content, the liquid they store can freeze, which can easily be deadly for your plant.