A continuity test is performed by placing a small voltage (wired in series with an LED or noise-producing component such as a piezoelectric speaker) across the chosen path.
If electron flow is inhibited by broken conductors, damaged components, or excessive resistance, the circuit is "open".
Devices that can be used to perform continuity tests include multimeters which measure current and specialized continuity testers which are cheaper, more basic devices, generally with a simple light bulb that lights up when current flows.
This can be done by placing one probe on the conductor in question, like a metallic chassis, and the other on a known electrical ground point.
In a similar fashion, on a printed circuit board, a continuity test between two solder points can give information on the traces connecting the components together.