The box on the right side of the dialog lists all of the available buttons you can add.
The box on the left side of the dialog lists all of the buttons that have already been added to the toolbar.
To add a button, find it in the box on the right, and click it to select it. Then click on the add button.
To remove a button, find it in the box on the left, and click it to select it. Then click on the remove button.
You can also add separator inbetween some buttons, to visually separate groups of buttons.