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I have a 69 - was able to lie on my back and look underneath. You can actually see the cable going into the back of the speedometer. There is small spring clip that you need to push in toward the back of the speedometer to release the cable (don't just try to rip it out of there).
On my 76 there is a spring clip as Witz described. If your car has AC you will need to pull the drivers side duct out to get your hand in to remove the cable. If the cable is out and you are patient you can feed it into the back of the speedo from behind the duct.
On a 68, it's threaded. It's a real bear to change. There is a steel crossbrace in there that literally butts up against the fitting. Changing those cables (tach, speed, trip) was the single worst thing I've had to do to my car. Plenty of cussing and cuts. Every time I got up under there, I'd knock some lightbulb socket or vacuum line loose and cut myself on some sharp screws or sheetmetal. Not enough room for a pair of pliers or a second hand to keep the threads aligned, either.