Heading sums it up. I'm using a 74HC04 to 'square-off' a sine wave,
but it's causing a fair amount of ringing on the output signal's highs
and lows which appears to be finding its way through to the eventual
final stage.

Paul-

Others have given good advice. Ringing is due to reactance, whether it is on
the power supply side or the load side of the chip.

Consider that the path between the 74HC04 and the following stage is a kind of
transmission line that has inductance and capacitance. It needs to be
terminated. I'm not sure how or if you can calculate the value of a
termination resistor, but you should be able to do it experimentally.

But, how do you know when you have reached your goal if the measuring
instrument introduces reactance? Perhaps measuring beyond the following stage
will provide sufficient isolation, in addition to using short leads as others
have suggested.

One other thought - would a plain 74C04 work at 8 MHz? If so, its slower speed
might reduce ringing.

73, Fred, K4DII