You do the registration papers before you go into labor, usually several weeks before you are due. That will include your info, insurance info, allergies, doctor info and a form stating if something were to happen would you want to be revived and or supported with machines. After baby is born you will fill out forms for birth certificate, possibly social security card (they may have you do that in the ss office later on) and if not married, the father will have to sign a form claiming the child as his (ours had to be notorized.)
Pretty much all that was stated in the comment above.
Lots of paperwork. Registration (which you can get and fill out at 30 weeks). Birth certificate, social security paperwork, if you aren't married there is paperwork for you and baby's father to fill out if he accepts paternity without DNA test. It had been 3 years since I last had to do it but I think there is more than just that.