Welcome to the AA forum.
How often does it happen? Oh, it's a bit of a crapshoot. Depends highly on the route, time of day, and passenger (especially elite) volume.
When "the system" determines that there will be unsold first class seats, even after processing all of the "standard" upgrade requests, you will sometimes get the offer from the kiosk. You will never be given the option when checking-in online from home, or, for that matter, if you speak to an agent at the airport. The charge will be $45.00 per 500 miles (or fraction thereof) flown. Since the distance from Tuscon to DFW is > 500 miles, but < 1000, you were charged $45.00 * 2 = $90.00.
I will admit that this is how I first experienced first class flying, and it quickly became addicting. But, the kisok didn't offer me very many chances. That's why I now strive to get to elite status....it costs a bit (but then again, doesn't any hobby?) and I find it very worthwhile.
By the way, if and when you do earn American AAdvantage status, not only do your chances of scoring an upgrade greatly increase, the cost is lower:
If you're Gold or Platinum, the cost is $30.00 per 500-miles flown; if you acheive Exec Plat status, the upgrades to first class are FREE!!
Enjoy!!
