I went in with my resignation letter with all the specifics in it - last day, reason for leaving etc, thanks for everything (i.e. nothing).
I just asked my boss if I could have a couple minutes of his time, of course he said yes, and I closed the door. I told him I'd been looking and got an offer and my last day would be XXX. We had a short dicussion about my reasons for leaving and he asked me if there was anything else I wanted him to know.
This is the time to give them some professional, respectful feedback on your experience with their company. There will be no repurcussions for you and I know as a manager, that the information is actually usefull to the company. Also, you can get it off your chest if the work environment was intollerable for you for whatever reason.
And that is it. Be prepared for them to accept your resignation immediately and ask you to leave immediately. Depending on what kind of information you work with, they may not want to give you a chance to take anything out of your office, besides your personal belongings.
At a previous job I had, if you were going the the competitor, you were escorted our immediately and all security revolked. It just depends on your job, the company you are going to, and your current companies policy.
If you give 2 weeks notice (which you should) and they ask you to leave, I think they still need to pay you through your notice time frame.
Just be respectful, honest and professional and it will be a good transition.
Congrats on the new job!