1) Dial a 10 digit number
2) Someone says "Hello, XYZ car service"
3) You say "I need a car at the corner of Sample street and 123rd road"
4) They say "5 minutes" and hang up
It takes the same or less time as using an app like Uber with fewer things that can go wrong.
One Saturday night we wanted to go out to a place 10 minutes away. We called a taxi cab around 7:30/8:00. We were told that it would be between 2.5 and 3 hours for a cab, if one came. We were considered "out of the way" when we were a 10 minute ride from downtown/the main bar area in the city. Forget about getting a cab back from those bars. We used jitney cabs all the time to get home. Yellow cabs wouldn't bother or were too infrequent.
There used to be a similar/related practice called "slugging" as well, it seems to have faded as Uber rose up.
With the Curb app, your request goes out to multiple cab companies and you usually get a cab that is very close.