The eggs usually hatch on the 7th or 8th night.
It is not particularly challenging, but it is a lot of work.
The baby fish will have to be removed to a separate aquarium as soon as they hatch. This separate aquarium should have all of the sides painted black and have nothing in it except an airstone. For the first 4 or 5 days, you must feed the baby fish live rotifers. But you can't just buy live rotifers at the LFS, you have to grow them. To grow rotifers, you have to feed the rotifers phytoplankton. You can buy phytoplankton at the LFS, but it is prohibitively expensive, so you have to grow your own phytoplankton.
Once the fish outgrow rotifers, they need to be fed newly hatched brine shrimp. You can buy brine shrimp eggs at the LFS and they are easy to hatch so this phase is pretty easy. After a few days of newly hatched brine shrimp, you need to start feeding them "enriched" brine shrimp. Brine shrimp that have been feeding on phytoplankton for a few days.
By day 9 they will transform in to miniature "fish" (before this they were larvae). And the hard work is done, you can care for them just like you would care for an adult.
This is just a brief summary. If you actually want to try it, I recommend you buy a book about it. Here are some good books to consider reading.
http://www.amazon.com/Clownfishes-C...7041/ref=sr_1_1?ie=UTF8&qid=1314663902&sr=8-1
http://www.amazon.com/Complete-Illu...7718/ref=sr_1_1?ie=UTF8&qid=1314663894&sr=8-1
