To use a timing light with a typical moped, you will need an external source of power. Timing lights typically require a twelve volt source of power like a car battery, so may need to tap off a car unless you are lucky enough to have a portable twelve volt power source handy.
Apply the black lead on the light to the negative terminal on the battery, and the red lead to the positive terminal, and clip the third lead around your spark plug cable.
To operate the device, remove your spark plug from the cylinder head, but reinsert the plug in to the boot at the end of your cable, and rest the working end of the plug against your engine somewhere in which it will be able to achieve a ground. If you do not ground it, the spark will not fire, and you could possibly damage your ignition system (or so it is rumored).