Divi doesn't have a built-in option for adding social share buttons, but there are several ways you can add social sharing buttons (for specific networks, or a general sharing button) to your Divi site.
Using a WordPress social sharing plugin shortcode
There are various social sharing plugins, such as AddToAny, AddThis and ShareThis, which allow social sharing buttons to be added via a shortcode. Once the social share buttons are configured in the plugin, a shortcode will be generated. This shortcode can then be placed in a Divi text module or code module, allowing the social share buttons to be displayed within a Divi Builder layout (e.g. in a post / page).
All of the above mentioned plugins allow you to add share buttons for specific networks (Facebook, Pinterest, etc). AddToAny and AddThis, I believe, also allow you to add a single sharing button (called the "Universal" button in AddToAny) that when clicked will offer the user a choice of places to share the content.
Using a Divi social sharing module
The Divi Social Sharing Buttons module is a third-party module for adding social share buttons in Divi. Once installed, it can be used to add social buttons directly in a Divi Builder layout (without the need to use shortcodes).
Displaying the social share buttons in the footer
If you'd like to display the social share buttons in the footer then, if you haven't already, I'd suggest switching from a standard footer to a footer created using the Divi Theme Builder. A theme builder footer is just a Divi Builder layout and as such you can lay it out and add modules to it in the same way as a regular page / post. Add a text / code module with shortcode, or a Divi Social Sharing Buttons module, into the footer where you'd like it to display.
If you'd like to include social icons similar to those displayed in the standard footer, then you can use the built-in Divi Social Media Follow Module (to which Divi Booster adds additional social icons).