The social icons in the footer are made with a navigation menu. If you’d like to add those, just create a separate navigation menu for them. Create a link to your page on the various networks you’d like to include using the custom link option in the menu builder. Save your menu and assign it to the social spot in the footer. For the most common networks, the links will be represented as an icon.
That’s what is built in to use. If you want to go beyond that, I would look for a simple plugin that adds icons via widget or shortcode. I don’t have a recommendation, but there are quite a few out there to choose from.