Ensure the amplifier is powered off. Connect a guitar to the input and press the amplifier power switch. Turn up the reverb control on the amplifier and listen for the reverb "echo" sound. Often, if there is a fault with the connection to the reverb tank, rather than within the tank itself, the reverb will be present, but very faint. If the amp has a reverb switch, ensure it is depressed. Some amps have a control dial and and on-off switch for the reverb. Tilt the amplifier back or forward and shake it gently. While doing so, you should be able to hear the "springy" sound.
Locate the reverb tank inside the amplifier. It is sometimes inside the upper "head" portion, in which case you should take your amplifier to a professional technician, as opening this part of the case can be dangerous. The tank is often housed separately from the main amp electronics, inside the speaker recess. In this case, the tank will likely be on the "floor" of the cabinet, keeping it low reduces unwanted vibration. There will be a pair of leads running from the amplifier to the tank. Ensure these are properly connected to the jacks.
Unscrew the brackets holding the tank in place and lift it out of the amplifier cabinet. If you have access to another amplifier of the same power and impedance, try connecting the tank to that. This will help determine if the fault is within the tank or in its connection to the amplifier.
Apply the continuity tester to the input and output jacks on the tank. There should be a complete circuit through the tank that results in the tester displaying a green light or sounding a buzzer. If not, there is a problem within the tank. Open the tank and check that the springs are properly connected to the power transducer at one end.
Determine which section of the signal chain is responsible for the issue. Most of the components involved can be purchased relatively cheaply from the manufacturer. The amplifier manufacturer can supply springs, leads and replacement tanks.