When Did Baptism Become Something Other Than Immersion?

I could ask how many have been baptized in a room full of people, and hands would go up. Then, if I ask them why they did it and how it was done, I might get an array of answers. Some would have been sprinkled while an infant. Others might say they did it as an outward sign of an inward grace. But does the Bible instruct us in these ways?