how the code actually links the button to the jlist1,
Not sure what you mean by "links".
You add an action listener to a button. When the user presses the button, the code in the action listener method is called where you do what you want to do to respond to the button that was pressed.
If you want to change the contents of a component like a JList, you need a reference to the JList object that you can use to call one of its methods.
NOTE: I see you are defining variables inside of the mehtods. When the method exits, those definitions will go away. You need to define the variables outside of the methods at the class level where they will stay around for the life of the class object.