Big island, Hawaii. Supposed to register your home birth before birthing (I didn't because I wasn't aware of this step so process will be different than my experience) I went after her birth. I had to take baby with me, provide proof from a medical professional that I had given birth, proof of residency at time of birth and at time of applying, two forms of ID, and a medical card for baby. Then fill out the application, pay the fee of $12.50, and send it off to Oahu. Takes 6 to 8 weeks to be processed and sent out.
Like insurance card, they use it as and ID for baby. Since there was no BC or SS# yet that's the only way for them to ID baby and make sure the baby is a U.S. citizen and not flown in from out of the country.