Here's How it worked at San Juan Capistrano on the Santa Fe:
There was a flag holder with two white flags in it* -- the same white flags that were displayed on the locomotives of Extra Trains. A sign on the depot displayed the schedule of trains for which Capistrano was a flag stop, and instructed passengers to step to the yellow line upon the approach of their train and to wave the white flag until acknowledged by two short blasts of the whistle. If flags were missing, passengers were to wave their arms. Encinitas had the same setup.
One difference between the two flag stop stations was the track speed. Due to nearby curves, the maximum allowable speed at Capistrano was 60 MPH, but Encinitas was in 90 MPH territory.
Don't panic yet. You can't flag a high speed passenger train in such short flagging distances. Engineers were required to approach flag stop stations at a speed that would allow making a normal stop at the station platform, until it was ascertained that no passengers were flagging the train.
* Supplying two flags provided prudent redundancy in case one became damaged. Both of these stations were in small towns in those days, and theft of the flags was uncommon. Special Instructions required Trainmen on passenger trains to observe that there were two flags in place, when passing flag stop stations. White flags were supplied on all locomotives and available at all on-duty points, and were replaced by the next train if required.