Static vs non static methods - best practice

I have a question with regards to program design.

If I have a class that looks something like:

public class SampleApp extends Engine implements Listener_OnMyEvent
{

  public static void main(String argv[])
  {
    int x=10;

    //Call metod1
    Method1(x);
  }

  public method1(int i)
  {
    //Call a method from the Engine Class
    //I know I don't have to have "Engine." here but it's just to
clearify
    Engine.method2();
  }
  public void OnMyEvent()
  {
    Log("Event Hapended");
  }
}

Let's say now that I want to move method1 to another class/file in
order to keep the code as neat and tidy as possible.

How should I do that? What is best practice according to you? Should
the methods there be static?

I tried to create:

public class MyMethods
{
  public static method1(int i)
  {
    Engine.method2();
  }

}
....but then method2 isn't available since Engine isn't implemented
unless I pass the whole class along:
MyMethods(x, this)

Is this correct?

I hope you see what I'm getting at here.
Any suggestions is appreciated.

Thanks