Order Management in Cart Ninja is fairly straight forward, each time there is an order on your website you will be emailed a notifcation (in addition to anyone else you set). You can then browse all orders on your website.
You can then see every order that is not marked as "Shipped" listed, note that orders are sorted by oldest placed orders listed first. This is because old orders are higher priority and should be shipped the soonest. You can see most recent orders by clicking on "New". There is other statuses that you can set the order to such as "In Production" or "Urgent", these statuses wont apply to every company but are there for your convenience.
You can click on an Order # to see the details of the order
You will be able to see Order #, Address the items they ordered, etc.. everything you need to complete the order should be listed on this page. After you fulfill the order you can click on "Edit This Order" and mark the order as shipped. It will no longer display on the Browse orders page except under the "Shipped" Filter or if you search for the order # / last name specifically.