It's pretty easy. I believe they've restricted it to one time per calender year now. You call them and set up a time, then bring the gun(s) you want to add (Unloaded, action open, in a locked case), and a money order for (I think?) $15. The form you fill out will give you the option of removing and adding, in case you are trading one for another. Last time it took about 7 weeks for them to call me and tell me my revised license was ready. You turn in your old one and you're set.
This is accurate. I just replaced one a few weeks ago. But . . .
After they take your money order and run your firearm, I had to schedule an appointment to requalify at Glen Helen. Same 10 rounds with a reload in between, 5 yards out.
You compete an index card, and he'll submit it to the department when you're done. Got the call to pick up the new card in about a week.