Mine did not go smoothly, but eventually worked...
I followed the instructions on the AT&T page posted earlier. Called that 800 number and entered the phone number for the phone that received the upgrade. Unfortunately, I was not given an "Option 2" of activating on a different phone number. I assume this was related to my premier/FAN status as I ended up in some business services section. After transferring to customer service, I got someone who was friendly but incompetent. She told me it couldn't be done. I explained that their website said it could and I would like to speak with someone else. She eventually decided she had figured out how to do it and took my IMEIs and ICCIDs for the swap. Took her about 45 minutes and several attempts, but assured me that everything was good and I should connect to iTunes for activation. iTunes still showed the wrong number, but she assured me that was OK. Then I got the lovely "There is a problem with this sim" message and no longer had phone service on either the old or new phone.
I was told that I would have to go to an AT&T store, pay $70 for a new micro-sim and $50 for a new sim for the old phone that was going to my wife. And that they would not release a micro-sim until tomorrow when the phone was officially released. Eventually I convinced her that I shouldn't have to pay and she put something to that effect in my notes, but that I would still have to wait.
Fast forward to me visiting the AT&T store 40 minutes later. Manager was excited to see an iPhone 4. Fixed everything in short order (although it took him 3 micro-sims to get it to work) and didn't charge me anything. Laughed that it would be ridiculous for them to charge me whether or not it was their fault. It is in their best interest for me to use my phone.
My advice: don't do this over the phone. And don't let them charge you for a sim.