For the most part you don't need to feed coral or nems. They are typically photosynthetic, they have a symbiotic algae inside them that provides nourishment to the coral (this algae is what gives the coral it's color). If you do want to supplementally feed do it sparingly and what to feed depends on the coral. As a general rule phytoplankton is probably best all around but with LPS
you can feed brine or mysis shrimp. Like I said phyto is generally the best, it can be available commercially or some LFS
grow their own which is live phyto. You could also get some from a local reefer. I just started culturing my own which is pretty easy. 2L pop bottles, air pump, miracle grow, light and of course live phyto. Phyto is also the food source of copepods which is what mandarin drogonettes eat.