It depends on the species of clownfish. The incubation times are relative to species and temperature of the tank. Ocellaris clownfish eggs hatch somewhere from 7-8 days while tomato clowns and red and black clowns take 8-10 days. When you start to see black/silver eyes start to develop on the eggs, you know it's time to pull out the rock and put it in the larval rearing container.
General guideline is that you need a 10g black round container for larval rearing (which is made special with a sump, for water quality control and temperature control.) For the first five days you would need to feed rotifers. Days 4-10 you need to feed unenriched Artemia. On days 6-15 you feed enriched artemia. On days 7-19 you will feed a weening diet of various fine flake foods, meaty shrimps, ... blended stuffs. Water quality is key... heavy protein skimming, daily water changes, and a fresh supply of foods.
After day 20, the clownfish are just big enough to transfer into an actual grow out rearing tank, which is 20-50g or it could even be a rubbermaid tub that is drilled for an overflow and a rubbermaid sump, just anything to keep them well fed and good water quality and temp controls. I've seen people successfully use stand alone plastic laundry wash tubs that have a PVC pipe screwed into the drain and a rubbermaid bucket underneath for a grow out system. It's cheap and it works.
As far as discussing how to culture phytoplankton, rotifers, and artemia - well, that's for another thread entirely.
The chances of your eggs actually surviving to adulthood are very, very, very slim and perhaps impossible, without specific care and systems already designed for it and your food cultured and ready to go.
