While the umbilical cord heals, your baby will only need sponge baths. Luckily, newborns don't get very dirty, so this should be fine for the first few weeks. Simply undress your baby, lay them on a soft towel, and wipe gently with a warm washcloth.

Once the umbilical cord has fallen off completely, your baby is ready for a real bath. It's best to gather everything you'll need so that it's within reach before you start. You might want baby wash/shampoo, a soft washcloth, and a towel. The bath water should be lukewarm and nowhere near as hot as we use for our own bathing. A strategically placed washcloth can be especially helpful for baby boys. (Warm water relaxes them and you might end up in the splash zone.) 

Read more tips on bathing your newborn at HealthyChildren.org.

Remember to never, ever leave your baby alone in the bath.