How can I check if an anti-static wrist strap works?

Solution 1:

Use an ohmmeter or multimeter to determine if there is conductivity between the metal part of the wrist strap, and the end part where you connect it to ground. You should see some measurable resistance (indicating good conductivity) if the strap is functioning correctly. If the resistance is extremely high (or as some meters measure, infinite), then the strap is broken.

Alternatively, you can just use it as a "wire" in conjunction with something else (e.g. an LED) and determine if you can provide power through the anti-static wrist strap. If current can flow through it, it's working, since that is all the device is used for (to provide a quick path to ground for your skin).

Solution 2:

Get a Van der Graaf generator and put your hand on it while you have your anti-static wrist band on (and shoes) and then get someone to go up to touch you. If they get a shock, it does not work. If your hair stands on end, that would be another sign that it does not work.

I have no idea where you could get a Van der Graaf generator, but this test should work if you manage to do so.