Gwen was in Peter's college class. That's how they knew each other. Yeah, he was in college.
He was in college during most of the first and all the second movies, can't remember if he had graduated by the third one or if they even addressed his education at all, but it's hard to remember anything about that movie beyond Jameson's scenes and Emo Peter.
And they confirmed that it won't be an origin story, to which I can only say THANK GOD. I don't think I could have made it through yet another retelling of the same story that every single person going to see this film pretty much already knows by heart.
Just letting you peeps know they confirmed it will not be an origin story a while ago. I doubt they'll even have a flashback.