Buttons[] Button = new Buttons[1];

creates an array that can hold 2 buttons but it doesn't create the buttons themselves which is causing the problem.

One other point - it is a convention that only class names should start with an uppercase letter so the array name could be confused with a class. Taking that into account I have modified your code to

1. Buttons[] button = new Buttons[1];
2. 
   
3. public class Buttons {
4.   public int x;
5. }
6. 
   
7. void setup(){
8.   size(480, 800); 
9.   button[0] = new Buttons();
10.   button[0].x = 10;
11.   button[1] = new Buttons();
12.   button[1].x = 50;
13.   orientation(PORTRAIT);
14. }
15. 
    
16. void draw(){
17.   fill(0);
18.   text(button[0].x,10,10);
19. }

Thanks, now I understand my problem.

Two things:

Also, you might reconsider your nomenclature. A class will create one object. So give the class a singular name, i.e. "Button". The array, which holds several elements, should be called in plural, i.e. "buttons".

I agree 100% with that.

A class normally a descrition of something we want to emulate in code. We can then use this description (class definition) to create as many objects as we like.

Wiki FAQ article: Why do I get a NullPointerException?