What is the safest way to give a baby a bath?

With Supervision. Children need to be supervised at bathtime. Do not leave your child, or even turn away, to answer the door or phone. Do not make the water deep, or too hot. Avoid getting water in mouth or nose, as this may frighten your child. Avoid getting soap in the eyes as this is uncomfortable.
Warm, shallow water. Once your baby's umbilical cord has fallen off it's time for his first bath. You can either use a basin with about 2 inches of water or a bath with an infant sling to support baby while he lies down. Use warm, not hot water (most baby stores sell tub thermometers that warn you if it's too hot). Then use a wash cloth and mild soap to clean him. Most importantly never leave the baby unattended.