Shooting newborns can involve some interesting challenges.
For one, you should not use a flash. A new baby is sensitive to light and flash after flash can disrupt their nervous system and might cause some eye issues later, though it would be hard to pin this to the photographer I would rather play it safe! If you bounce a flash you are alright, but it is still not recommended. Depending on where you shoot (at home, the hospital, or on location) you can move the baby to the light, use a higher ISO or shoot RAW. Saving low light photos is one of the best features of RAW imagery. While it will take more memory, this feature might also have your back.
Secondly, it is usually hot in newborn baby’s rooms. They are figuring out life and their temperatures change quickly, and then they cry. Keeping the room nice and toasty keeps the new life comfortable but can mean embarrassing situations for the photographer who is up and down and all around the room working out. Dress in comfortable clothing, preferable breathable and sporty!
The other challenge can be the parents themselves. If they are new to this experience and to holding newborns, the shoot can take a longer than you expect. Encourage the parents to take the time they need to move and adjust the baby, but make sure and leave extra time to schedule these shoots. When you can and it is appropriate, step in and help. But, always respect the parents wishes when holding their little one. Rushing adds stress for everyone and these moments are precious and take time.