This is going to depend on your situation, but in most cases - wherein the mother and the baby are both healthy and mom and/or dad are capable - feedings and diaper changes will fall to you. You are the kid's parent, after all.
They may do one or two diaper changes depending on whether there's a nursery and whether your baby is in it. And if there isn't a nursery and your baby rooms in, they'll likely put on a fresh diaper after the first bath (if you want them to give LO the first bath there). Other than that it's all you.
As for feedings, if you decide to formula-feed they may do one or two feedings, again depending on the nursery situation, but the bulk of the feedings, whether formula or breast, will fall to you as well. If LO is in the nursery they'll bring the baby to you for feedings. I mean, even if there is a nursery the baby will still spend most of his/her time in the room with you.