How do I get rid of the default widgets in the widget areas to add my own?

he widgets that you see in the widget areas if no widgets are selected are placeholder widgets. It is there just to show you that you have indeed place too add widgets there.

The Widgets are controlled by what is called a if statement, and basically reads that if there are no widgets added, put the placeholder widgets there. If widgets are selected add the widgets that was selected.

In order to add your own widgets to the widget spaces, you just need to add your widgets in the widget areas specified on the widget page, and they will show up instantly, and the placeholder widgets will be removed.