To see your 'Orders', from the store dashboard go to:
> Orders

From within this page you can see all the customers who placed an 'Order' with you and their status will be pooled at the top in various categories for quick and easy access:

Clicking on an orders 'ID' number will open up another page with more information about the order:

Here you can learn what the customers email and/or phone number is (useful for retargeting), what their shipping address is (useful for analyzing where the bulk of your orders come from), the payment status, the amount paid, and what was purchased.
The 'Order from AliExpress' button can be used to process your orders (the customers details will be filled in automatically):

The 'Send shipped email' button can be used when all items have been shipped:

The 'Send shipped email' can be edited by following this guide.
Below the order details under the heading 'Products', you'll find 'Ali order ID' and 'Tracking ID'. These will be updated automatically after the AliExpress supplier receives the order (Ali order ID updates) and ships the item (Tracking ID updates):
*If the 'Ali Order ID' and/or the 'Tracking ID' doesn't update itself automatically, you will have to manually fulfil these IDs yourself*

Each item purchased by your customer will have its own unique 'Tracking ID' as different products come from different suppliers that ship separately.
The 'Activity' heading at the bottom of the page shows and dates the order process:
