Cell phones are a required tool in dealing with a flat tubular. Usual
approach is as Hillrider describes.
I used tubulars exclusively for racing and fitness riding from 1974 to 1999. Never carried a cell phone, never rolled a tire, even on one 55 mph descent into Estes Park on a warm August day (without a helmet, no less). I still use one set for riding my old steel bikes on nice days.
Got and fixed lots of flats, though. If I got one, I used my spare, and if that went flat (rarely), got a loaner from a companion.
My latest discovery is a tube sealant made by Tufo. It works really well on small punctures such as those made by goat head thorns.
I wouldn't go as far as to persuade people to switch to tubulars, but in my opinion the horror stories are grotesquely exaggerated.