Go to one of those newborn classes and learn how to change a diaper and swaddle at the minimum.
(If applicable) split the night into two shifts to maximize uninterrupted sleep.
Listen to your gut. You're ultimately responsible for your baby. If something doesn't feel right, then speak up and set boundaries with the other people in your life. Do it from the start, preferably. But if you get talked into something you later change your mind on, then say so and enforce those boundaries.
(If applicable) when you get back from the hospital, the mother will need a prescription filled. Bring her and the baby home, and then figure out all the prescription stuff that day for her. Read all of the doctor's orders and then later when she gets some rest, summarize them for her. (E.g. if she nurses, she may need to stop some prescriptions.)