I've been stuck out in Western Canada most of my life, and yet managed to see tours of Spider Woman, Phantom, Parade and the Canadian sit down production of his Show Boat. Just saying
As Gaveston said, a number of people on here could probably give good answers to specific questions, but it's kinda hard to know where to start.
One thing that comes to mind is that he very much needs a concept for his shows--and preferably a political one it seems. His flops often seem to come about when he doesn't find one (like with Merrily--actually in that case it was more a muddled mix of concepts). He famously didn't reallyget Sweeney until he saw that he could use his industrial revolution concept. Equally famous is his quote to Lloyd Webber when asked to do Cats--I don't remember it word for word, but essentially he asked if it maybe had something to do with Queen Victoria, and was a metaphor, and ALW replied basically just saying "Hal, it's about *cats*".
If you have time, aside from the books mentioned by Gaveston, there are two pretty good bios of his work: Harold Prince and the American Musical Theatre and Hal Prince: A Director's Journey. EVerything Was Possible about the making of Follies aso gives great example of his process.
For what it's worth, he's my fave director who wasn't also a choreographer (if that makes sense).