Go to your town hall. Fill out paperwork, present proof of pregnancy and proof of residency
New Hampshire - no proof of pregnancy or involvement of any medical professional required at all. Call vital records and give them preliminary information. Vital records sends a notification with preliminary info to your town clerk and also send you the birth information sheets to fill out (mom can fill out and sign as her own attendant, no other witnesses are required). Make an appointment with the town clerk and bring baby with you. Clerk will review forms for completeness and send back to Vital Records and the birth certificate is then usually available to get copies of within two weeks.