First call the EXP desk as the flight is the most important piece of the puzzle. Then go to GA or F ticket counter if vouchers are required.

I'll give an example:

Early this year we were flying (IIRC) LHR-DFW-SJC (or something like that). Well, the LHR-DFW a/c was leaking from the lav area. After a couple of hours, they scrapped the flight, and told people to go to desk XYZ for rebooking for the next day.

En route I called the EXP desk. They rebooked (and confirmed upgrades) for LHR-ORD, that day and ORD-SJC early the next morning, and arranged the vouchers, telling us where to go to get them.

While folks were still filing toward desk XYZ, we did an about-face to the new gate and boarded our plane shortly thereafter.

Cheers.