When you list on the 800 number mentioned above, be sure to get your confirmation number. That way, you can bypass the ticket counter agent by entering the number into the Kiosk. Just press "Yes" when it asks you if you've got a paper ticket with you. That'll eventually be the Captain's J/S form carried by crewmembers.
If you can't do the Kiosk thing, the conf. # will help immensely with the gate agent in bringing up your record. Last resort, if they look you up by your last name, be sure they do so spelled FD(lastname)...FD preceeding your last name...that'll save a LOT of hassle, too.
The gate agent should have a clue, but if not, they should issue you a boarding pass with a seat number. One copy of the J/S form should be attached to that for their records. I think they keep another copy, and at least one copy goes back to the CA so he can replace it with a new form.
Best point of advice is to get to the gate reasonably early enough to catch the crew before they get to the plane, or enough time that the gate agent will be willing enough to round-trip to the airplane to get a J/S form for you....i.e. not boarding or nearing boarding time.
I commute on AC a lot, and Jazz every so often and the experience has been top notch. Lately, though, there seems to be something up with the FAs not letting J/S'ers in open 1st seats, let alone their own non-revs. Not sure what's going on...