Ava here from Shopify :)
Was this product ordered via Oberlo? If so, there is a guide here on how to get tracking updates on the order! This guide will also show you how to update your customer's shipping update, so this tracking link will be emailed to them even if they have not set up a customer account.
If this order was not placed via Oberlo, can I ask how you are fulfilling your orders? Are you working with a fulfillment centre or a courier?
Let me know and we can take things from there!
If the customer has added an email to his order, they will get a notification of the order shipping. If they click on the link "View your order", they will end up at the "Order Status Page". You should also be able to email them the "Order Status Page" which can be found in the Customers Order > More Actions > View Order Status Page. Copy the link and send it over to them.
On the customers order:
Edit: Alternatively, you will need to install an app that allows the customer to search for the order at their end via your website. Most of those apps require that you use an email and order # to look up the status of their order. The current ones available also seem to charge a fee: https://apps.shopify.com/search?page=1&q=order+lookup&st_source=