If you find yourself in a situation where you need to turn around in a hurry, the quickest and simplest way to turn around is to do a forward 180. Performing this maneuver consistently and accurately takes practice, but hopefully this video gives you a solid jumping-off point from which to try out this maneuver in a safe location before challenging yourself with narrower roads and different surfaces.
The simplest way to do a forward 180 with a car is to use the handbrake, and the first step is always to slow down to an appropriate speed for the surface (30mph on pavement, less on gravel or snow). With that accomplished: crowd the right side of the road, clutch in, pull the handbrake, and turn left. The vehicle should start to rotate and as it does, shift your eyes to the side window so that you can see the road ahead (which was very recently behind). Once you have roughly 90 degrees of rotation, release the handbrake, select 1st gear, release the clutch and drive away. In an automatic, the maneuver is the same except you can simply stay in Drive or shift the automatic if you choose to.
The reason for crowding the right edge of the road and performing the maneuver as a left turn is simply because here in the US, we drive on the right side of the road and this allows for the most room possible to execute this maneuver. Once you are proficient, definitely get comfortable performing the forward 180 to the right as well, so that overseas, in confined quarters, or in any other special circumstances you know that you can do a forward 180 in either direction comfortably and confidently. The forward 180 is the same whether performed to the left or right, the only consideration would be shifting your eyes for the exit.
Without a functioning handbrake the best bet is to use the pendulum turn. This will require much more practice to execute consistently with precision, but a rough series of events would be: Approach with more speed, lift, turn in the opposite direction you hope to do the 180, and apply some brake to transition weight forward. If you do this correctly, the car will rotate. When it does, release the brake and turn back the intended direction for the 180. The energy that you have stored in the springs will rebound and the vehicle will start to spin around. Use a little brake again to create more rotation if necessary, get it in first gear, release the clutch and drive away.