This is probably a dumb question, but don't judge.  How can I tell on a 1968 corvette which battery cable is negative and which is the positive cable?

Red=positive/hot.  Black =negative/ground.  Black is bolted to the body. 

Typically, the battery itself will have a "+"  either stamped or embossed onto the battery by the positive terminal. Same with the negative side, with a "-". If the battery is not in the car, on most Shark era cars, the Positive cable is on the "driver side", and the negative on the "passenger side", of the battery as it sits in the well. Of course, as Mark points out MOST cables or cable ends are color coded, red for positive, and black for negative. If all else fails, you can trace the negative cable from the battery box to right under the driver side seat, as the negative cable goes from the battery directly to frame, under the driver's seat.

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"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"

Take an ohmmeter and measure each one to the frame.  The one that measures the lowest is the ground cable.

1973 L-82 4 spd