If your contrast is not changing when you turn your potentiometer, you need to check your potentiometer. Connect your potentiometer wiper to analog pin 0 and run this:
If your reading on the serial monitor goes from 1023 to 0 when you slowly turns the pot, you have a working pot. Anyway, you have not told me what value of pot you are using. The suggested value is 10-25K ohm. I've used 100K ohm once and it worked ok, the contract is just not very stable.