Google for pictures of the stabilizer so you'll know what you're looking for. It's a rectangular metal can about the size of the end of most people's index fingers. It will have spade lugs coming off of it.
Once you've located the stabilizer look carefully at the circuit board with the spade lugs coming out of it. One pair of lugs will be labeled "B", that's the switched 12V "battery" connection. Make sure that with the ignition switch on you find 12V there. If not trace wires back to the fuse box to see where you're loosing power.
The other pair of lugs on the stabilizer will be labeled "I" for the the "instrument" connections. As the DR said, you MAY be able to put a volt meter on there and find about 10V... but don't count on it. Digital meters may not detect the voltage at all or may bounce all over the place. It is best measured with an analog meter (with a needle). However, sometimes that doesn't even work.
If you find that you have 12V at the input to the stabilizer and can't detect any voltage output, it's easy to make a modern replacement. For purists I put together a PDF on how to make your own solid state stabilizer and re-package it inside the Smiths stabiliser box. See:
https://home.mindspring.com/~purlawson/files/SmithsVoltageStabilizer.pdf
However, since the stabilizer is hidden behind the dash and this should be a negative ground car, the easiest and cheapest repair is to buy a 7810 chip from a source like Mouser.com, solder flying leads to it, cover them with heat shrink tubing and attach it to the firewall. This approach will cost you more in shipping and time than the cost of the actual parts (and still cost less than a NOS Smiths stabilizer). A JPG of this simple fix is viewable at:
https://www.adocars.com/elf/v-reg.jpg
(Thanks to my friend Wes for the JPG).