You would need to create a shipping address table. the shipping address table should contain a foreign key relationship to the users table:
shippingID - Pirmary Key
shippingUserID - Foreign key to users.userID
You will need to make sure that the user is logged in before they can add shipping addresses. see the "How to apply Login/Register functionality to your Checkout Process" tutorial in the How To section of the eCart support page:
When the user logs in, a session variable will be created with the unique primary key from the users table. In the Add Shipping Address form, store that session variable in the shippingUserID column.
To display a select list with the different shipping addresses the have entered, create a recordset the queries the shipping address table. Filter the shippingUserID column on the userID session variable.