The potentiometer does not connect to "Volts." That is, it doesn't connect to the power supply. Vin is signal in, not volts in, "signal" being the square wave that you want to amplify.
Explanation: Vin means signal (input), while Vs or Vcc means power supply.
So one side terminal of the pot connects to ground, the other side terminal then becomes Vin and connects to your square wave generator (oscillator), and the center terminal connects to pin 3 of the LM386. Thus you turn the pot to vary the input to the LM386 from zero/ground to maximum.
Probably correcting the Vin connection will solve your present distortion/feedback problems. But...
<< a lot of feed back and distortion when I connect the Potentiometer to ground as well as connecting the 10k capacitor between pin 1 and pin 8...This is happening before the oscillator is connected to the amplifier... >>
As audioguru points out, the capacitor between pins 1 and 8 increases the gain of the LM386. No capacitor, the gain is 20. Capacitor added, the gain jumps to 200, which is a big jump. Too much gain could cause both distortion and feedback, so remove the capacitor (but first correct the Vin connection of the pot).
Explanation: Gain and volume are not the same thing, but you could think of them as the same in this (only this) case. If this were an audio amplifier then the capacitor between pins 1 and 8 would set the total output power available (20 or 200), and the pot would set the listening level (However, the "20 or 200" is not watts, or output power, or something else: it's gain).
All of which bring us to a pretty big confusion. Editing your statement for clarity:
<< a lot of feed back and distortion...This is happening before the oscillator is connected to the amplifier... >>
This is confusing because it's impossible as stated. "Feedback" is, by definition, an amplifier's output becoming its input, so the amplifier runs wild, infinitely amplifying its own input until things break. But if there is no input--the oscillator is not connected--then there can be no feedback.
Also, distortion, by definition, occurs in an amplifier (in this case). But if there is no input--the oscillator is not connected--then there's nothing to distort.
However, I think this is a confusion in use of technical terms, and the problem is again the wrong Vin connection. If the power supply were connected to the amplifier input (as it apparently now is), then the LM386 would be trying to amplify its own power supply, which would certainly cause some strange things to happen. Again, correcting the Vin connection would fix this.
Sadly, connecting the power supply to the amplifier input (Vin) might have burnt something out, you might have to build another LM386 amplifier. Or maybe not, of course. We hope for the best.