what do you have so far? Take a look at the processing examples under the serial I/O library. specifically the simplewrite example. That is probably a start or what you are looking for

this is an example:

1. import processing.serial.*;
   Serial port;
   
   void setup()
   {
      size(200,200);
      port = new Serial(this, "COM13", 9600); //change COM13 to your Arduino USB Port COM
   }
   
   void draw()
2. {
3.    fill(255);
   
4.    rect(100,100,100,100);
   
5. }
6. void mousePressed()
7. {
8.   if( mouseX > 100 && mouseX < 100)
     {
      if( mouseY > 100 && mouseY < 100)
      {
       port.write(1);  //in arduino 1 = led on
      }
     }
   
9. }

You need to make sure what form of "1" your Arduino is expecting. Is it reading ASCII, hex, int, etc.,.....? Test your Arduino code with it's terminal to make sure the LED is turning on/off as expected, then replicate the serial output in your Processing code.