She went outside and 'hailed a taxi'. [=waved or called for a taxi to pull over and stop]
The pilot 'taxied' the plane out to the runway.
We caught/took/got a 'taxi' to the restaurant.
(..) get the cup of coffee, had picked up the lady who was going shopping, who had missed getting the earlier cab. Taxi had to stop for a man crossing the street, who had left for work minutes later than he normally did, because he forgot to set his alarm. (..)2008 The Curious Case of Benjamin Button
(..) on the phone, Daisy was rehearsing for performance at the Paris Opera House. And while she was rehearsing, the woman, off the phone now, had gone outside to get a taxi. Now a taxi driver had dropped off a fare earlier, and had stopped to get a cup of coffee. And all the while (..)2008 The Curious Case of Benjamin Button