To create a new shopping basket, first click into the shopping basket page (use the "My Basket" link).
Look for the "Basket Settings" section of the shopping basket. Enter the name of the new shopping basket in the box and click the "Create" button.
Your new basket will show up at the left side of the page as shown below.
You may now click on the shopping basket to view its contents (it will be empty until you move something to this basket).