How can I PWM 4 LEDs from 0 to full brightness using a two axiz resistive joystick?
There's a number of steps you need to go through:

Read the ADC to get the joystick position
Subtract 50% of the full range (512) to get a ±512 value
Note the sign to get the direction
Take the absolute value to get the distance
Subtract a small amount to create a &quot;dead zone&quot; in the centre of the joystick
Map the result to 0-255 for the PWM.

The code might look like (note: untested):
int y = analogRead(0);    // Get the current value
y -= 512;                 // Subtract 512

int pin = 2;              // Unless otherwise told, use pin 2
if (y &lt; 0) {              // If it's negative...
    pin = 3;              //    then we'll use pin 3 instead
}

y = abs(y);               // Take the absolute value (discard the sign)
y -= 20;                  // subtract 20 for a dead zone
If (y &lt; 0) y = 0;         // zero any negative
y = map(0, 492, 0, 255);  // map the new full range of 0-492 to 0-255
analogWrite(pin, y);      // light the LED on the pin we chose above.

And do the exact same thing for X with different pins.