The first challenge is getting viable eggs! This is the most frustrating part imo. You just have to wait (maybe years) and hope that you are providing your fish with the right environment to spawn. And are you sure you have a male and female and are they sexually mature? There have been other posts describing differences in sexes of zebrasoma so this will probably not be as difficult as some other species.
Yellow tang larvae have been raised to several weeks post hatch. I had a link to the page which included pictures of the yellow tang larvae at every day. Unfortunately that link doesn't work anymore but I think it was the Oceanic Institute in Hawaii that posted it. From what I remember their first food was basically from a wild plankton tow and they never found a specific species of copepod that worked. I think they got the larvae at least to metamorphosis and maybe even through it.
For feeding, yellow tang larvae are very small so all strains of rotifers are too big. You would need to use copepod nauplii or ciliates as a first food. Unfortunately many larvae are very picky eaters and even if there is a suitable size food available they don't always eat it. Copepod eggs (A. tonsa) are available from online vendors now so it is possible to get copepod nauplii production started with less effort than in the past but who knows if yellow tang larvae will even take them. There are also harpacticoid copepods available online and their nauplii might be a good first food too.
As far as food changes, you just offer them the next size food and if they take it that's probably a good indication that they are ready for larger food. A.tonsa will grow quite big to their adult stage so I would imagine that they could stay on them for a least a couple of weeks or even months (that is if they will eat them to begin with).
It was already posted earlier for you to check out marinebreeder.org. There is a ton of information and knowledge there.