What is the Meaning of Baptism in Christianity?

What is baptism? When people say that when you’re baptized, the old, sinful person dies and emerges from the water to walk in “newness of life,” what does that mean exactly? And what happens if we stumble in our Christian walk after we’re baptized?
Is there more than one way to get baptized, or does the Bible tell us how it should be done? And does it matter?