When a new order comes in from a customer, the first thing you'll want to do is set the order to 'Processing' so that the customer feels comfortable about their purchase. Then, it depends:
1. If you have the product inventory on hand, you will then start preparing the product/order to be sent out by your local post or shipping company of choice. Once the local post ships the product, you'll want to change the status of the order to 'Shipped' that will send out a notification email to your customer.
2. If you are dropshipping, you'll go to your product source and order the product to be sent directly to the customer's shipping address. Once your supplier ships the product, you'll want to change the status to 'Shipped' that will send out a notification email to your customer.
Please check out the video below to get a demonstration of what to do with a new order if you are dropshipping (as described above in scenario 2):