For audio and composite video: Don't. If you must, use a resistor to bleed charge, and a small cap for RF bypass if appropriate. Anything more invites ground loop.
Other devices, especially stand-alone equipment that doesn't need to be connected with other grounded devices:
My preference is to use a screw as chassis grounding (or several for RF), using at least a perimeter ground like so,
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which is good enough for single sided, low speed circuits. The perimeter is more for convienience, as you can return grounds to it as you go.
A full ground plane is better:
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(Same board, top side. This serves for illustration purposes.)
Better still, both sides (as above, or):
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Note the screws in four corners, providing extra RF grounding (not visible are the aluminum standoffs grounding the bottom side -- I don't have PTH boards).
Since signal ground is chassis ground, ground loop, RFI and so on are minimized (assuming you didn't royally screw up something else). The circuit is doubly safe, because loose wires short to ground, which is ground ground, which is also safety ground (assuming you go on to use a three wire cord).
Tim