Once they have started hatching, I usually leave them in the incubator and keep a close eye on them until they look like they might be ready to take a nose dive into the vermiculite (what substrate are you incubating in?) They usually emerge with their yolk sac still exposed so they need to be on a clean, damp, non abrasive surface. So, usually when I pull them out of the incubator they are still in the egg and I make a nest of damp paper towels in something like a margarine tub. I usually keep each egg/baby in its own tub until the yolk sac has flattened out, when the yolk sac is larger they are vulnerable to injury by another hatchling.
So, when the yolk sac is flat, but the opening in the plastron hasn't completely healed, I'll put them together in a plastic shoebox on several layers of damp paper towels.
When their yolk sac is down some, but not quite flat, I'll usually start soaking them every day, in a shallow jar lid.
Another thing I've been doing since last year (and I've been meaning to post about it) is that after they leave the egg shell, I rinse it out and clean it and put it back in with the baby. They will nibble on it, sometimes completely consuming it over a couple of weeks. I first noticed this last year when I didn't remove the egg shells as quickly as I had previously. I have to think that they must do this when they stay in their nest (in the wild) and it must be intented as a source of calcium for them. This year I noticed some babies starting to nibble on their egg shell before they left the egg. I usually don't try to feed them until they are at the point that their yolk sacs have flattened out and they are with their siblings. Then I offer small molted mealworms (these will be white) and small earthworms and I also will put sticks of reptimin in their water. If you have sowbugs/pillbugs (also known as roli polis) they love these also, if you can find some small ones. Its important not to panic if they don't eat right away, some just don't. I have a group of 5 that hatched about 4 weeks ago and there is one that just doesn't seem interested in eating yet, although I think he has probably eaten some eggshell.
Once their plastrons have completely healed, I put them in a 10 gallon tank with 3-4 inches of damp bedabeast.
I put a shallow plant saucer in for a water dish. There are many other options for substrate, but this is what I do.
They reallly like to bury themselves and I think this is good for them and probably what they do in the wild. I usually pull them up (if they are buried) every other day and make sure they get in the water and I offer food. I write more about this in an earlier post. There are several good posts on hatchling care in this forum. I would read through these and then ask questions to "fill in the gaps".
I'll also post a link to a good site on box turtle care.
Good luck and keep us posted!
Box turtle breeding/hatchling care