[time / event] + 之前 / 之后,+ [clause]
之前 / 之后,+ [clause]
之前 means "before" and 之后 "after". Both go after the event or time they are measured from, and the whole phrase comes before the main clause.
English puts "before" and "after" in front. Here they follow what they refer to.
At the head of a sentence, with nothing in front, 之前 and 之后 point back at a moment already in the conversation: "before that", "after that".
以前 and 以后 do the same job after an event, and are more spoken. The difference is the bare word: 以后 alone means "in the future", from now; 之后 alone means "after that", from a point in a story.