Basic sketch to demonstrate analog input.

analogRead.ino

int ledPin=9; //Variable to store pin of LED
int potentPin=A0; //Variable to store pin of potentiometer
int potentValue=0; //Variable to store last known value of potentiometer
int brightnessValue=0; //Variable to store LED brightness

void setup() {
  // put your setup code here, to run once:
  pinMode(ledPin, OUTPUT); //Setup LED pin for output
}

void loop() {
  // put your main code here, to run repeatedly:
  potentValue=analogRead(potentPin); //Read the value of the potentiometer pin
  brightnessValue=map(potentValue,0,1023,0,255); //Map the potentiometer value to a brightness
  analogWrite(ledPin,brightnessValue); //Set the brightness of the ledPin
}