Multiplexing potentiometers
There are a few ways of doing what you want.  One would be to use an analog multiplexer as in this answer: Expanding analog inputs to the Arduino

Another would be to use digital I/O pins to control the power and ground to the potentiometers.  Note that both sides of the pot need to be controlled, not just one, since any connection of one will interfere with the other.

So you will need four IO pins - one for the +5v and one for the GND of each potentiometer.



In this example set D3 to OUTPUT and HIGH, D4 to OUTPUT and LOW, and D5 and D6 both to INPUT.  You will now be reading from the top pot.

Then change D3 and D4 to both be INPUT, and D5 to be OUTPUT and HIGH and D6 to be OUTPUT and LOW.  You will then be reading from the bottom pot.

A bit wasteful of IO pins though.