Whenever a customer sends a message or opens a dispute, a store administrator will see a notification about it on the homepage of the store's Admin area:
To access the messages themselves, click the respective link ("Messages" or "Disputes"). It will forward you to the Messages page of your store Admin area (Orders -> Messages), where you can process incoming requests from your customers:
Another way to see incoming order messages is when working with the order details. While on the order details page, you will know you have new unread messages/disputes submitted regarding the current order if a small number label displays next to the Messages tab title. The number on the label will show the number of unread messages.
X-Cart will notify you about any new messages/disputes via email.
A store administrator receives notifications on the email address specified in the "Sales department emails" field in the Store Profile.