As much as you can, try to use natural light. You do not have to be an experienced parent or a rocket scientist to figure out the fact that flash basically translates to sporadic extremely bright and artificial light. That is something that newborns do not like. It will startle them and might leave them crying. If they are fast asleep, it may be something that might wake them up and unless you already know this, it is not a very good idea for you to wake up a sleeping baby, much less a newborn, for that matter.
Another thing that you would need to consider especially if you are photographing the baby with the parents is that it brings them a situation that feels contrived and choreographed. It is something that can totally ruin the vibe especially if what you are going for is something that is natural and candid. Do your best to position the area that you are shooting in somewhere that can provide an abundant amount of natural lighting like a window or a door or somewhere open, bright and airy. As much as possible, dark and stuffy studio settings are something that you should veer away from, if you can help it.
Be adaptive and flexible
You should go well out of your way to be adaptive and flexible enough for whatever scenarios you might be dealt with at some point. What you need to know right from the start is the fact that literally anything and everything can happen when you are dealing with something as unpredictable as newborn photography. You will have unexpected visitors one way or the other and not all of them will be pleasant. There is an extremely high possibility that you will be barfed on, pooped on, spat on, and so on and so forth.
Ask a newborn photography expert who has been there and done that and they will surely tell you that they have experienced anything and everything under the sun. It is extremely important for you to stay calm and pretty much take everything with a grain of salt at some point.
Schedule in the morning
Try to schedule your newborn photography sessions during the mornings as much as you can and try to coordinate this with the parents. If there anything that you would need to do and make sure of, it would have to be scheduling your time schedule around the baby. Mornings are usually the best times for you to initiate the photo shoot. The baby has just been recently fed, probably also recently bathed, and most probably sleeping almost all of the time. This is the best a time as ever for you to set your photo shoot schedule to.
Babies also tend to become more agreeable and tend to have a really great disposition when it is during the morning. If you go ahead and schedule your photo shoot sometime later than after lunch, they tend to become crankier and may break out and cry or throw a tantrum. Any parent will tell you that that is not something that they would advise at all.