When connecting a potentiometer with a logarithmic taper, how does one connect it. I made an amp circuit and originally used an linear pot. Then, I think I just got lucky with replacing it with an logarithmic pot.

In the obvious case, how is it connected as a volume control to input into an amplifier IC such as an LM386?

I figure that placing the wiper in the middle position, the resistance measurements from the wiper to each end will be different. Those measurements will differentiate which end to connect to ground and the input signal.

Can you clarify this for me.

 

Yep. The low ohms end goes to ground.
or, look at the way the handle will turn for "volume down" and you can imagine looking through the front of the cabinet and see, with pins up, the wiper will be at the right pin for zero volume.