Juvenile daisy parrotfish start out life as carnivores (when they are still under 30mm long). Their main food sources at this point are protists, foraminifera and dinoflagellates. Then they become omnivorous when they add zooplankton to their diet.
Adult daisy parrotfish are strictly herbivores. They use their "beak" (fused pharyngeal teeth) to scrape of algae from dead coral and rock. When grazing, they actually bite off parts of the coral and crush it into fine sand. This sand is then excreted into the water. A large parrotfish can excrete over a ton of sand every year! Daisy parrotfish are always eating because being herbivores means that only 35 to 50% of their food is being digested. This is due to the fact that algae have cells with cell walls, making them difficult to fully digest. For more information on how adapt to "going vegetarian" see my Adaptation page!
When snorkeling or scuba diving you can actually hear these guys bite of pieces of coral and crush it in their mouths. So when snorkeling, if you hear a crunching noise, look around there might be a parrotfish nearby!