Lots of people kill plants with kindness; keeping the soil moist (rather than wet) is a good rule of thumb unless it’s something like bamboo. It's better to underwater than to overwater your plants. Succulents store water in their leaves and stems. Let the soil go dry before thoroughly watering them. Water your plants in the morning, so that excess water can evaporate.
Don’t fertilize for the first 2 or 3 months, as most nurseries/suppliers pot their new plants in a soil/fertilizer mix. After that, fertilize most plants each time you water with a quarter-strength soluble fertilizer. Although succulents generally need less fertilizer than other plants, feeding is necessary for healthy growth. Check your local nursery for something with low nitrogen content. Feed your succulent plant fertilizer in the spring.
Light can be an issue for some plants. If you see leaves turning brown or getting very light green, they’re probably getting too much sun. If they lean toward the light, they probably need to be a bit closer. Very few plants can take direct sunlight, particularly from a west- or south-facing window. If you must use these windows, try putting a sheer curtain on the window to cut down on the intensity of the sun. Succulents, like other plants, need plenty of light. Succulents grow better if they don't cook in the sun.
Humidity is also a factor to be considered; if the tips of the leaves get brown, or if they wilt quickly, it may be too dry. To combat this (without using a humidifier), try setting the pot on a tray or saucer filled with pebbles, into which water has been poured so that the pebbles are just sticking out. As the water evaporates, the air immediately around the plant will be more humid.
If you are having pest problems, a good drench will sometimes take care of things and most nurseries can point you at a good all-round product (Safer Soap is a good one). These are all very general suggestions, obviously, but hopefully they’ll get you back on track with your plants.
Sometimes your plant may need repotted, pruned, or thinned. These are actions that can be done less frequently to keep your plant happy. Often times you can tell when your plant might need this extra TLC by appearance. Long, straggly, pale vines? Time to cut back some. Outgrown its pot? Time for an upgrade.