I did this when the 3gs was announced. When you order your iphone online it asks if you are a current at&t customer or if you are gonna open a new account. When you choose new account it will ask if you want to port a number over, if yes then it asks for the telephone # and your account number. After that you pick what plan you want etc and once you order it your pretty much done. I ordered from apple.com btw.
Once you receive the phone you plug it into your computer and activate it via itunes. It'll ask for your phone number, last 4 of your social and zip code. When i did this in less than a minute my new iphone was activated and the phone itself will say your phone is now activated. Once you do this your verizon contract will automatically cancel. I tried making a phone call with my verizon phone and it wouldn't let me and told me to get a hold of customer service.
Overall extremely easy process and activation was seamless, i couldn't believe how quick it activated considering i activated it on the 19th when the phone came out.