In the wild, looking for food is one of the three things that saltwater fish do (the other 2 are reproducing and staying alive or not being eaten by a bigger fish). The argument could be made that being caught by a collector is the same as being eaten.
Feeding Your Fish
If you watch saltwater fish for a while, especially in the wild, you will notice that the herbivores are constantly looking for food or "grazing" as some people say, the carnivores pretty much just cruise around, passing up easy meals. Herbivores, such as Tangs, have a longer digestive tract than carnivores. This is because it takes longer to digest algae in order to extract the protein required for the fish to survive. Carnivores have a shorter digestive track because it doesn't take as long to extract the protein from the flesh of another critter (snail, fish, shrimp, etc.) to keep them healthy.
Herbivores, ideally, should have a constant food source available to them. The algae that grow in your tank will provide a certain amount of this, but unless you have a lot of it, you will need to supplement their food supply. Prepared foods, such as many flake foods, are concentrated food and (depending on the type) can supply the fish with everything they need. Feeding your fish a little bit of food once or more per day is closer to the way they eat in the wild than feeding them a bunch every 2 or 3 days.
Most fish (even sharks) will only eat what they need to survive. If you watch your fish when you feed them, you will see that they will actively eat for 2 minutes or so, then ignore the remaining food for hours. The food that remains in the tank is wasted and will end up on the bottom of your tank, creating even more nitrates.
If you only feed your herbivore fish once every 2 or 3 days, it is not the way most fish eat in the wild, which is what we should try to duplicate as closely as possible. In my experience, feeding twice per day, only what is consumed in about 2 minutes has been the best. This gives the fish what they need to remain healthy and at the same time doesn't create any maintenance problems in the future such as more water changes to reduce nitrates created from uneaten food left on the bottom of the tank.
Carnivores, on the other hand, are a different thing. Eels are an excellent example. They will go for days without eating, then suddenly feed voraciously for a couple of minutes. It has been my experience that if you have a mix of carnivores, omnivores, and herbivores in your tank, they will all find and eat what they need if you feed lightly twice per day.
What Food and How Much
The Marine Fish Food Comparison Chart is a good place to start if you are interested in finding the best food for your critters. If you examine the contents of the commercially available saltwater fish foods, you will find that there are three basic formulas: those containing mostly algae, those containing mostly seafood such as shrimp, krill, mussels, squid and various fish. The third contains a combination of the first two. There are also a number of frozen fares available which are excellent sources of protein.
We have found that most herbivores will consume or at least pick at many of the frozen foods, such as Mysis, brine shrimp, and the others once they are used to eating hand fed foods in an aquarium. We have also found that new arrivals to an aquarium pick up on eating foods in an aquarium is they see other fish eating it.