The order API (Application Programming Interface) is implemented as an XML based webservice. This service only available to Premium accounts.
The location of the web service is:
The request should be a form POST and must include the following fields:
username - Your shopping cart username
password - Your login password
version - Should be set to the value 1.0
You can refine the orders listed by setting limits:
start - The lowest Shopper ID in the result set
limit - The maximum number of orders to list
The maximum limit is 300, this also being the default. So if you have more than 300 orders in Admin then you will need to make a second request, in other words, you will need to page the results.
Finally, you can specify the order, they are ordered by Shopper ID (usually the same as date but not always):
orderby - ASC or DESC (accending or decending order)