Bad ground at battery, as DJ stated, or a partial short to ground, as Ed stated. Try the ground connection first. Remove, clean, re install with electrical grease. Inspect the ground cable, it could be bad. Add a second ground cable that goes directly to the engine or transmission. Inspect both connections to the battery. Use electrical grease there too. Once you know all is good there and you still have low voltage, then start disconnecting things until the voltage comes up. Start at the end of the line and work towards the battery. The last thing you disconnected is the fault. Start at the alternator or generator cutout. If the voltage come up then start checking the lights, stop switch, and horn. You can use your ohm setting to check these things. Also suspect is the light switch.
I am assuming you are testing the voltage with the points open or a piece of paper or cardboard is placed between the points. Or the ignition is off.
Does the starter crank the engine over well? If it does then the ground and battery connection should be good.