Newborns' skin (especially the face) is prone to peeling and irritation, and isn't always quite as beautiful as you might expect in the beginning. You may have to hold out until baby's around 4 months to see that soft, airbrushed, magazine-baby skin.
At birth, baby's skin will appear to be dry. Since baby has spent the last nine months surrounded by amniotic fluid, his or her old skin wasn't able to flake off like an adult's does. So now baby's basically in the process of peeling off all that skin (like a sunburn). Baby's skin also starts out very translucent, so you'll be able to see lots of birthmarks. As baby grows and the skin gets thicker, many of those marks will seem to disappear. In fair-skinned babies, you may often see a red mark between the eyes (an "angel kiss") or on the back of the head or neck, on the eyelids, forehead, nose or upper lip (known as "stork bites"), which also becomes less noticeable over time. Next time your boss or partner gets mad, look closely though—you can still sometimes see these marks in flushed or angry adults!
In general, baby's skin doesn’t need much specialized care...just a lot of TLC. A mild cleanser is safe, though many people recommend just plain water. These days, baby wipes—especially ones for sensitive skin—are so gentle that they're generally safe to use once baby hits the one-month mark. Babies' faces and genitals can use daily cleaning, especially in urban areas (like Manhattan, where I practice), for obvious reasons. Baby's face takes a lot of abuse (just think of all that spitting up and drooling!), so do your best to keep it clean and dry. If baby's skin seems excessively dry, irritated or itchy, or if you notice a rash or breakout, consult your pediatrician.