There are 2 ways to add social links to your templates. Either through the Dashboard or in the Builder.
From The Dashboard:
You can add the URLs for your social icons in the Company Settings of your dashboard.
You can get here by clicking "Settings"
Then click "Company Settings"
Scroll down to "Social Links" and here you will find the area to add your social links.
Once you have added your social links, be sure to click "Save" at the top. In order to reflect these changes in your Shopify notification emails, you will need to set your templates live in Shopify again.
From The Builder:
Click "Template Footer"
then "Social Icons"
Then "Edit social links"
Once again you will need to set your updated templates live again in Shopify to reflect these changes.