A newborn's nails grow quickly. To trim baby's nails, use baby nail clippers, nail scissors, or a file. First, give baby a bath to soften his nails (and hopefully make him sleepy). Then lay him down or sit him in your lap.
Press each finger pad away from the nail so the nail sticks out. Snip just the white part, leaving a bit so you don't accidentally cut too low. Expect to do a trim two to four times a month. You should only have to cut baby's toenails once every few months.
Before he sprouts teeth...
By wiping baby's gums, you'll get him used to the habit of daily teeth cleaning, which will make it easier to enforce brushing down the road. Wrap your finger in a bit of damp gauze or a washcloth, then swipe it over baby's gums. You can do this as often as twice a day. No toothpaste is needed at this early stage. Keep it up even after baby's teeth begin to erupt (around 6 months). You don't need to switch to a toothbrush until after the first couple of teeth have come in.
After he sprouts teeth...
Once baby has a few teeth, it's time to get him used to a toothbrush. Let him chew on one as he would a teething aid. After his first birthday he can imitate you brushing your own teeth. Either way, you'll still have to wipe baby's teeth yourself, either with a soft, baby-specific brush or damp gauze.
The more teeth he has, the more serious your brushing efforts will have to be to get rid of food particles and bacteria. Once all the baby teeth are in, you can begin using a tiny drop of toothpaste -- just get a pediatrician's okay first.
After a bath, gently clean the outside and back of baby's ears with a moist cotton swab. The important thing is to avoid pushing the swab into the ear canal: It can damage the eardrum and even cause hearing loss. Removing the wax isn't necessary; earwax protects your child's ear canal by sealing out moisture, dust, and bacteria. (Besides, scraping it out often just causes the ear to produce more.) If your child has excessive earwax that you think might be interfering with his hearing, consult your pediatrician.
Baby's first haircut -- even if it's just to trim a few wisps out of her eyes -- is a milestone. Here's how to make the cut: