I have tried with my clownfish. You will need to culture live phyto, rotifers and baby brine. The rotifers eat the phyto, and the baby clowns eat the rotifers for the first couple weeks, until they are large enough to eat the live brine.
It took me over a month just to get these food sources to a good level (you need to make sure you have enough, or else the baby clowns will starve to death), so unless you have them going already and have a good stock on hand, you probably won't be able to raise the current batch of eggs.
And I would also caution you to let your clowns lay eggs for a while before you try to raise the fry. Mine laid every 10 days for 4 months. Of course, as soon as I got all my rotifers, phyto and brine going, they decided to stop. They went for about 4 months and didn't lay anymore, and only started up again in the last month. I want to try to raise their fry, but because of what they did last time, I'm waiting at least 6 months before I put all that money, effort and time into getting their food going!
It can be expensive to set everything up. You will need several small grow-out tanks for the fry, and several buckets and containers for the foods, lights, pumps, airline tubing for the phyto, a rotifer sieve for the rotifers, several culture bottles for the brine... I have a thread dedicated to rearing my tomato clown fry at another site, PM me if you're interested. I can also give you details on where to buy all the supplies. I have lots of the "phyto fertilizer" left that I'd be willing to sell if you want (you need "fuel" to feed the live phyto cultures).