She can't just give you the baby. You both have to get a lawyer to draw up papers, petition the court, prove that you have adequate means to support the child and have a social worker examine your home and check your background to be certain the baby is going to a good home and not a child predator. Usually the social worker at the hospital and child protective services will arrange for foster care while those issues are settled. Full custody usually takes anywhere from 3 months to a year, because the mother is usually granted a short period where she can change her mind.

To do any kind of adoption, you will need to complete and pass a homestudy. If your friend wishes you to adopt her baby, I would advise her to seek out a family lawyer to make sure that the entire process is legitimae and to make sure that she completely understands the process.