you don't have to feed them unless you are talking about non photosynthetic corals like tubastrea.
if you want to feed them, they eat meaty foods. some folks use pellets, some use thawed mysis shrimp from the LFS
. i like to use fresh fish from the supermarket. it's the same thing i feed to my omnivorous fish.
chopped clam, shrimp, scallop, or squid tubes will all work.
whether you feed them or not, you'll need ample lighting to support them.