In order to work in Neonatal nursing, you need to be a Registered Nurse. That means that you will attend a 2 year college to give you an Associate Degree in Nursing or a 4 year college to give you a Bachelors Degree in Nursing. Which you chose depends on your long range career goals. Suffice it to say that if you choose to get a BSN, you will have many more options in the future.
After either professional preparation, you will be eligible to take an exam (called the NCLEX) in order to be licensed to practice nursing in the state in which you will work.
As with many professions, you need to obtain the overall knowledge before you can specialize in Neonatal Nursing. When you have been hired, and I strongly recommend working for a teaching hospital that offers a new grad internship/preceptorship, you will attend classwork in neonatology, and work with a more experienced nurse until you are able to function independently.
As a neonatal nurse, you will assess and care for premature and sick term infants, and their families. Depending on where you work, that will be in an acute ICU setting, or in a less acute "convalescing" setting. You will work with MDss, Respiratory Care Practitioners, Social Workers, Occupational Therapists to provide that care. You will take vital signs, listen to the babies heart, lungs, and abdomen, gently examine them from head to toe. You will monitor their oxygenation. You will perform venipunctures to obtain blood, start IV therapy, and give medications. You will change diapers, weighing them to monitor the babies fluid balance. You will test their stools for blood to ensure that the baby is tolerating their feedings. You will give feedings, either by nipple, or via a tube into their stomach. You will help Moms breast feed, and teach them to take care of their baby. You will need to be aware of the babies developmental needs, too.
It can be a very satisfying job, but it can also be very sad. Babies who are in NICUs die sometimes, and you may have to comfort a family whose child has died, you may even have the priviledge of holding an infant who is dying. In this process, you will also make sure that the baby and his or her family have whatever spiritual support they might want.
Good Luck in your career endeavours!