Are you transferring your number? If so, you don't even have to call them to deliver the news. Let Verizon port your number... then its done. You can call them just to confirm you want to end your account, but there shouldn't be much hassle at that point.
If you have a separate number with Verizon, you will need to call and cancel. Just be friendly and firm. Even say up front your decision is already made and you'd like to save everyone's time and not hear about your option of staying with AT&T.
I wouldn't do any more than answer one question about why I'm switching... too many dropped calls or whatever. And after that still be friendly but let them know you're not interested in talking any further about it.