Snapping turtles hatch in the wild after about, on average, 80 - 90 days, but with higher temperatures it might even take only around 60 days. Some 'turtle mothers', when not having the chance to lay eggs one year, might overwinter the eggs and lay them the next year.

In captivity, the hatching usualy takes place within those limits, although many people report 60 - 80 days on average.

After hatched in an incubator, the hatchlings should stay there and be left alone for a day or two. Then, removed to a temporary plastic box with damp pieces of cloth or a towel, again, left for 4 - 5 days to let them use up their yolk sacs. Only after that, the snappers will be ready to be placed in a regular, water filled setting.
( Different turtle species require different type of environmnt. Wrong habitat could kill the hatchlings - for example tortoises can not be put in water and the other way around, water turtles can not survive without it. If you are not sure what kind of turtle do you have consult someone who knows, and if the knowledgeable person or the book are not around - turn to the internet, talk to people at turtle & tortoise clubs, societies, breeders, forums, chats, and definitely do some keyword search using as many as possible search engines )

For snapping turtles, and water turtles in general, the tank set ups basics are not different from the description made in the heater, water etc. chapters, except that some extra care should be taken in maintaining the quality of the water.
Make sure that the water is clean ( install a filter or make changes whenever dirty ), warm ( set to proper temperatures - usually 25⁰C or 80⁰F ). The tank doesn't have to be very big, but there should be some space left for decorations ( which will not work well with bigger snappers ) like rocks ( no sharp edges ), driftwood, branches, partially submerged to give the little ones some hiding places ( turtles like privacy - like us ! ), and also some places to climb for basking.
If there is no direct sunlight access ( never put the whole set up in direct sunlight ! Make sure that one area of the tank is in shade and only the area designed for basking stays in direct sunlight ).

The best, although not cheap, option is to buy a full spectrum basking light. My snapping turtles were regular baskers as babies, spending hours at a time stretched out on the branches of a large, interesting piece of driftwood.

If you don't have a glass or acrylic tank, use quite cheap plastic stock tanks for small animals ( sold at pet stores ) or any other plastic containers like those designed to store your things at home.

Feeding:
snapping turtles are carnivorous ( meat eaters ) and also most other aquatic turtle species supplement their diet with an occational meat meal. The hatched turtles should be fed with a variety of insects, earthworms, mealworms, small crickets etc.. Also small pieces of raw red meat and fish - just like larger turtles.
An occational leaf of spinach, cabage or lettuce should be placed in the tank - they like an accational veggie snack.
Also, the commercially available turtle foods can be purchased and given to the turtles as supplement to their natural diet ( it is not a good idea to raise the turtles exclusively on the commercial diet - it might lead to health problems later in life ).

The small turtles should be fed everyday, as much as they would eat. When hungry, they might start biting at each other, which might turn dangerous especially in set ups with a whole bunch of them ( once bitten by one turtle the others will most likely start doing the same thing evantually seriously hurting the unfortunate one, possibly killing it ).

The snapping turtles grow very fast ( see the growth charts ) and begin to bite at some point. The first bites by small turtles not a big deal, but they still it hurt... )

Well then, have fun when they hatch !