How To Make LCD Shield Button Code Work with Pot
I think what may be most helpful is an explanation of some tools which would serve you well on this.  In order to use the potentiometer to select different options, a simple solution would be along these lines:


Read the potentiometer value.
Check which range the value fits in.
Perform a corresponding action.


Here is one idea for accomplishing this:
Read the potentiometer value:

int reading = analogRead(A0);


Check which range the value fits in.

if(reading &lt; 1023/4){
    //Action 1
}else if(reading &lt; (1023/4)*2){
    //Action 2
}else if(reading &lt; (1023/4)*3){
    //Action 3
}else{
    //Action 4
}


Perform a corresponding action.

//Do something cool.