Thats a pretty loaded question.
The short answer is, stable high quality water parameters and lots of light. The light part can vary between different coral types as they are different levels of photosynthetic, but the water part is a universal truth.
You need to keep all the key components high (calcium, magnesium, etc) and all the bad components low (ammonia, nitrite, nitrate, phosphorus, etc.) Plus you need a very stable temperature and salinity level. Regular testing and digital tools will help you get things accurate. Keeping a "reef log" next to your tank where you write down all the test levels can also help you track how stable your tank is.
Lots of testing, lots of water changes, and things will start to take off, and you can do less testing when you get more "in tune" with your tank.
If you have more specific questions about a certain type of coral, post that along with any other relevant information.