In general, grounding problems fall into two classes.
OVERALL GROUNDING: Every conductive surface on the turntable needs to be brought together on a single ground bus, and a wire taken from this to the chassis of the receiver or integrated amplifier. A hum due to some disturbance or interruption in this area will appear in both channels, and will be heard in addition to the music. The most common causes of this type of hum are: (1) lack of a ground wire; (2) broken or loose ground wire; (3) failure to properly connect the arm to the ground bus.
CHANNEL GROUNDING: This will usually result in one channel humming, not both. Common causes are: (1) bad audio cables; (2) open coil in the cartridge; (3) a loose wire at the junction point between the signal wires coming down the arm and the audio cables; (4) bad wiring in the cartridge carrier; (5) oxidation of the mating contact plate at the end of the arm.
Now . . . a cautionary note. Do NOT chase down the hum with a naked ohmmeter. If you hook an ohmmeter current across the coil of a phono cartridge, you can damage the coil. Always insert a dropping resistor in series with one lead of the ohmmeter. I like to use 220,000 ohms or greater. With a decent ohmmeter, 220,000 ohms indicates a short, 220,750 ohms (or thereabouts) indicates good continuity through the coil, and infinity indicates a loose wire or open coil.
Best,
Fred Longworth