Set up the apparatus as shown in the sketch.
Move the pin in the cork up or down until there is no parallax between the pin and its image. At this point the pin is now at the centre of curvature of the mirror. Measure, carefully, the distance between the pin and the back of the mirror. This distance is the radius of curvature of the mirror. Half this distance gives the focal length of the mirror.
If you like you can see an animation that shows the experiment: