Get some help with other stuff round the house for the first couple of weeks. This is where your or her parents (or both) can be invaluable, helping with housework and cooking meals to give you both a chance to rest.
Even if it’s just for an hour, take baby for a walk or to do the shopping and leave Mom to have a lie down in the afternoon. This will earn you extra brownie points, plus you get some Daddy time.
If you’ve got a spare room or a comfy sofa, sleep there for a couple of nights during the week if possible. You need to help her as much as possible, but no one’s going to thank you if you get fired for sleeping on the job. Then you can take over at the weekends.