From what I have seen and read, clowns are one of the easier species to breed. The mechanics of it involve several tanks, a REALLY good water purification system, and the willingness to stay on the job while you are hatching the young. First feeding is very important. You will also need culture systems for algal and rotifer feeds. Decapsulated Artemia cysts are a good thing to have around as well. You have to know when to feed the young and what to feed them. They are small enough that they will only be able to feed on certain organisms of the right size. Because they are so small, their energy requirement (metabolism) is very high and feeding them at the right time is the difference between good survivability and a tank full of dead larval goo. There are some good mass culture feeds on the market.
Oh yeah. Don't forget about collecting the larvae. You can do it with an overflow or you can do it with a flashlight and a beaker. Depending on the intensity of your culture method, you may want at least two larval rearing tanks set up. Higher intensity culture means more larval rearing tanks required. You will need to maintain the temperature of the tanks within about 0.2 degrees C at 28C. Too cold and they will die...too hot and they will die. The 28C temperature is a good round number that is easily maintained. Culture of other species of fin fish tends to maintain temperature at that setting too, but I have seen LRTs at 30C as well.
The main thing you need to have when culturing any fish is a buyer for the end product. What are you planning to do with the young that you produce? Granted, the cost of raising clowns isn't that high, but why even do it if you don't have a buyer for your product? Clowns are very prolific. I read somewhere that one laboratory culturist of Premna (maroon) clowns recorded a gross survivability of >4200 juveniles. Realize that this number was attained under very tightly controlled lab conditions that require very expensive equipment to maintain. Do your homework first and see where you could sell your product. Otherwise you will have several tanks full of juvenile clowns that have to be fed to survive...and that my friend co$t$ money.