Please keep in mind that many plants will have their own unique care such as light, water, soil requirement but this will be a quick guide on succulents in general. Each unique care will be noted on each plant's profile.
BRIGHT. BRIGHT BRIGHT BRIGHT BRIGHT BRIGHT. Many succulent failure comes from keeping plants in shade. What we see as bright might not be enough for plants. There are some succulents that prefers more shade though such as Huernia, Stapelia, Rhipsalis and other understory succulents but most succulents will prefer more direct sun than shade. If you notice an abnormally fast growth in your indoor succulent: check to see what kind of light it is getting, maybe it becoming etiolated and seeking more light.
Succulent watering is another touchy subject but in general they will require a bit more water during their growing period and pretty much left completely dry during their dormant period. More plants rot during dormancy than any other time so if the soil is moist, just leave it alone. If the soil is dry during growing period, leave it for a few days then water thoroughly and allow plant to dry up again.
Fast-draining soil is the key to happy succulents. Some plants, like Sedums and Sempervivums, can grow on wetter media but in general it is better to pot your plants up in free-draining soil or add pumice, pearlite, or sand to your potting soil or obtain succulent-specific soil.
Note: It is better to pot your plants in pots with a drainage hole