How did we come to have our current alphabetical order?

I was reading about someone who was shocked to discover that the alphabet actually had an order, and it got me thinking. How did the alphabet get the order that it now has? I understand why it is ordered—ordered lists are easier to remember, and it helps organizationally. However, I don’t understand how we got the order to begin with. I assume that written language began to develop before a formal alphabet was in place, so people would have known the letters before they were put in order. Who first decided what order to put them in, and how did that arrangement become standardized?