Your newborn may come home with puffy eyelids and swollen breasts. Not to worry: The first is caused by fluid she's retaining to tide herself over until feeding is established, and the second comes from your hormones, which were passed to her before birth. Both will disappear on their own. Some infants have fine hair, called lanugo, covering their bodies; this will fall off within the first few weeks.
Don't expect to play peekaboo just yet: During the first week, your baby will sleep at least 12 hours a day, up to four or five hours at a stretch. Quiet and active stages of sleep alternate every 30 minutes or so. Quiet sleep is characterized by regular breathing and very little movement, while the active stage includes irregular breathing, body and facial movement, and (experts believe) dreaming.
Newborns spend about 10 percent of their time in a "quiet alert" state--calm and attentive, with their eyes open. The quiet alert stage is a good time to let baby get to know you. Hold her and let her study your features at close range--infants can only see objects 12-15 inches away. Make small facial movements, and see how she responds. Babies tend to tune out when stimuli become overwhelming, so don't be offended if she needs to take a break after a while.
Note: The information above offers general guidelines, but all babies develop differently, and few hit their milestones precisely when the conventional wisdom says they should. If your child was born prematurely, you may want to use your due date as a baseline for following baby's development.