You can check your AT&T upgrade eligibility by dialing *NEW# (that's *639#) to request a free text with your eligibility status. The phone will display "Thank you, your request is being processed. A message will be sent to your phone." Expect a text within a few minutes.
If you bought a day one iPhone 4S, your upgrade-pricing will likely kick in on May 8, 2013.
Other readers are considering the jump to new carriers. TUAW reader Bill Burgess made his switch after the 4S debuted. Verizon ported him over the same day, and AT&T just billed his last month and early termination fee.
TUAW readers Patrick McCarron and Jeffrey Vargas point out that Verizon has a 14-day return window. This allows you to delay porting your number, meaning you can test the service before switching fully.
Chris Kapusta adds, "If you're not one to just jump in the water before checking for sharks, you can have Verizon assign a new number, and once you're satisfied with the service, port your AT&T line at a later date. There should not be a charge for doing this."
He points out that you should not cancel your AT&T service directly. Allow it to switch over automatically as part of your port. "If you cancel before the port is done, your number is gone forever."
He suggests you make sure you know your AT&T billing password, and ensure that your contact information is up to date. This information must match what you give to Verizon, or the port will fail. Luckily, Verizon (and most carriers) offer a dedicated porting support team. If something does go wrong along the way, they have experts that can help.
K2 Kevin points out that you should make sure to check coverage in your area. Most carriers offer coverage location tools. Here are AT&T's and Verizon's. Kevin points out snarkily that, of course, whatever area is not covered is likely where you're moving to for the next two years.
Chris de Jabet over at Techese offers a great write-up about pre-ordering an iPhone 5 while switching to Verizon. Go check it out.