Not much to it really, she's doing most of the work! 
Keep some free-choice feed and fresh clean water available close by so she can quickly gobble up some food and water when she leaves the nest to eat/drink/poop/exercise.  As for the eggs, if any start to smell or ooze gunky stuff then get rid of them before they contaminate other eggs.  If you notice her repeatedly leaving a certain egg out in the cold, on the outskirts of the nest, get rid of it; she knows it's infertile and/or going bad.  Also, the eggs will be very greasy from her body oils by the time hatch day arrives, this is normal.
As for the nest, yes, the chicks will likely fall to the ground if you don't modify the nest.  I had a hen, unbeknownst to me, go broody on top of a stack of round hay bales.  I found out when I happened to go in the barn that day and heard a momma hen clucking.  Found her on the hay bales with a single chick under her and several more 10' below her on the ground, all dead, poor things.  But what I've done that has worked real well when a hen goes broody in a nest box up off the ground is I just cut a piece of cardboard to line the front of the nest, cut to be about 4" taller than the nesting material, to keep the chicks in.  It lets the hen out but keeps the chicks in.  I mostly do this because I have opportunistic barn cats who would show up quickly if they heard a lost lone chick peeping loudly for its mother from the floor of the coop.  Once the hatch is done, I move the family into a cat-proof brooder area.