You're standing on the corner trying to hail a cab and a black car (or random sedan) will pull up, wind down the window and ask if you need a taxi. It's usually off-meter so the rate is negotiated/paid in cash. If you sound foreign (as I do), the rate is usually pretty high unless you argue it down. It's risky, tiring and makes you thankful for industry regulations that make licensed taxis a fair and predictable commodity service.

Taxis in New York (including Ubers) are required to have a special license plate. Also taxis looking for passengers illegally will honk at people who look like they might need a ride.

Not sure about in NY, but in SF, Uber cars tend to have a small (maybe 3"x3"?) but visible sign in a corner of the front windshield. Similarly, Lyft cars tend to be have a little glowing mustache and/or a similarly sized sign in the front.