1. ArrayList.remove(int index)

or

1. ArrayList.remove(Object object)

Could you give me an example of this? This doesn't seem to work for me.

I'm not quite sure where you want to remove the item from the ArrayList... The ArrayList in question would probably be missilelist.

I used this bit of code here:

missilelist.remove(randomMissile());

But nothing happens in the program, no objects are being removed.

EDIT: I'm using an 'if' statement in the update function to create a condition for it to be removed. The if statement works because I've tested it with other functions.

Full game below:

1.     class Missile {
         float endX;    // End X position
         float endY;    // End Y position
         float endvarX;  // Line gradient X
         float endvarY; // Line gradient Y
         float startX;  // Start of missile line
         float startY;  // start of missile line
   
         color c;
         Missile(float init_endvarX, float init_endvarY, float init_startX, float init_startY,
         color init_c) 
         {
           endX = init_startX;
           endY = init_startY;
           endvarX = init_endvarX;
           endvarY = init_endvarY;
           startX = init_startX;
           startY = init_startY;
           c = init_c;
         }
   
         void render() {
           {
           smooth();
           stroke(c);
           line(startX, startY, endX, endY);
           }
         }
   
         void update() {
           endY = endY + endvarY;
           endX = endX + endvarX;
          
           if (dist(endX, endY, posX, posY) <= 15){
           missilelist.remove(randomMissile());
         } else{
         }
         }
        
        
       } // class Missile
   
2.  
    int framestore; // frame last missile was created on
    int Mdelay;     //delay between next fire time
    int posX; //mouse X position of player
    int posY; //mouse Y position of player
    float fireX; //starting X co-ordinate of player missile
    int fireY; //starting Y co-ordinate of player missile
   
      
       Missile randomMissile() {
         return new Missile(random(-2.0, 2.0), random(0.5, 2.5),
         random (200, 600), 0,
         color(random(0, 256),
         random(0, 256),
         random(0, 256))
           );
       }
      
       ArrayList<Missile> missilelist; // list in null initially
   
       void setup() {
         size(700, 500);
         framestore = 0;
         Mdelay = (int)random(60, 150);
         missilelist = new ArrayList<Missile>(); // creates and initially empty ArrayList of missile objects
         frameRate(30);
          
       }
   
       void draw() {
         background(255);
         if (Mdelay < (frameCount - framestore) ) {
           for (int i = 0; i < (int)random(3); i = i+1) { // gives the initial value of 0
           // then randomized between 3 maximum values. This means there can only be between 1 and
           // 3 missiles active
           // then adds +1 to the value of i, but cannot be more than 3.
           // code courtesy of Jacques
             missilelist.add(randomMissile());
           } 
           framestore = frameCount;
         }
        
         // render all the missiles.
         for (Missile b : missilelist) {
           b.update();
           b.render();
     
       
         }
         fill(255, 80, 80);
         triangle(350, 480, 335, 500, 365, 500);
        
        
        
       }
      
       void mousePressed() {
       fireX = 350;
       fireY = 480;
       posX = mouseX;
       posY = mouseY;
      
       smooth();
       strokeWeight(2.5);
       stroke(255,0,0);
       line(fireX, fireY, posX, posY);
       }
   
   

remove() removes an object in the list. randomMissile() creates a new missile object, thus it won't be in the list. If you want to remove a random missile that is in the list, then pick a random int between 0 and the list's size.

I'm still totally stuck. I don't know what to do with my code at all.

Actually, you should move the collision test to draw.
      for (Missile b : missilelist) {
        b.update();
        b.render();
        if (dist(b.endX, b.endY, posX, posY) <= 15){
        missilelist.remove(b);
      }
      }
(untested)
Hint: Ctrl+T (or Edit > Auto Format) helps in getting a good vision of your code.