If you buy a tracking label through the Shopify store, tracking is available for some mail classes on the order status page to your customer and also through the order section of the admin.
Not all shipment types include tracking, which you'll be able to see in the order history and you can confirm here by clicking the Quick Compare button- https://www.usps.com/ship/insurance-extra-services.htm
At the moment, the order status page is only fully supported for USPS shipments just so you know!
You can read about the order status page here as well- https://docs.shopify.com/manual/shipping/status-tracking
We're building out a complete package tracking solution, which we're offering for free right now. It currently works with Amazon Alexa, and we'll be adding email & SMS options, as well as a status page (supporting all shippers that we track, which is ~400), and Google Assistant integration.
Please check it out and let me know if you have any questions.
If you are using FedEx to fulfill your orders, you can use the FedEx Rates, Labels & Tracking app which helps you print labels as well as handle FedEx tracking.
Using the app, you can print the labels for all your orders in bulk. Once you print the label for an order, the app generates tracking number for the order and send it along with the shipping confirmation email from Shopify.