How does a person get sworn in during a courtroom session? (Pretty please with sugar on top...read the questions in the details.)?

In the US, at least in the past, a person put their right hand over a copy of the Bible and was asked, “Will you tell the truth, the whole truth, and nothing but the truth, so help you God?”

Does this still happen today? What if the person isn’t Christian? Does that make it null and void? What is the protocol in other countries during a court proceeding? One inquiring mind would like to know.