My spider plant got damaged in a move and when my kitten sat in it I have been babying it, when do you cut the babies off and how do you replant them?

If the babies have little root nubs, they are ready. Some people like to put them in a little cup with the root nubs sticking into the water a little bit, some like to put them directly into soil.

If you put a baby on the soil surface with the root nubs touching the soil while it is still attached to the mother plant, it won't suffer a dehydrated period like some babies can do when their nubs don't grow into roots very quickly.