I just did this with a family member on a completely differnent account. It's easy if:
1. You're giving an iPhone 4 to the family member, and taking "their" 4S. (since they both use micro-SIMs)
2. You and the family member are in the same location at the same time of the swap
Here's the easy steps.
1. Activate the new iPhone4S right out of the box. This will immediately deactivate your relative's old phone and SIM. don't bother plugging into iTunes - just do the on-screen activation all the way through until the phone is able to accept calls under your relative's #.
2. Turn off the new phone, pop out the SIM
3. Do a full erase of your old iPhone 4 (make sure you're backed up first!)
4. Turn it off, pop out it's SIM
5. Swap SIMs into each phone, turn them on, plug into the appropriate computers with iTunes for each phone, or do an iCloud restore, if you're backed up there
It worked fine for me - no need to deal with a trip to an AT&T store and/or clueless salespeople.
Of course, if you're trying to swap with a phone without a micro-SIM, or you're not able to meet in person to do the swap, you'll have to invovle AT&T