In order to allow your customers to purchase items via the e-commerce feature you must create individual user names and passwords for each account.
Instructions
Go to Setup > Users on the main menu and click on the "customer" link. Then click on the green "Add E-Commerce User" button.
Type in the information requested (customer, email, user name and login). You can also add some notes if necessary.
Once you click "Save" the system will automatically send and email invitation to your customer with the instructions as well as the username and password needed to login to the e-commerce.