To allow customers to see a list of orders they've placed, first make sure that Public Profiles are enabled. This will display a public "Members" page at the top level of your site.
Then set "Enable Order History in User Profiles" to Yes. You can find this option at Dashboard > eCommerce > Settings > User.
Users who are logged into their site will then be able to visit their own profile page and see a subpage named "Order History":
This page will list each order the user has completed while logged into your site.
Click any order's row to see details of that order.
Clicking this button will send a duplicate of the entire selected order to the checkout. This feature is handy for customers who want to repeat purchases.
This link will display a summary of the order details in a lightly-styled format for ease of printing.