So ...

Upon activation, go to Appearance => Menus.

All you need to do, is to add new custom link menu items to your existing main menu.

Needless to say, you'll have to add your own custom links for each social media platform separately:

Once you have entered the link text and your custom URL for the given social platform, click the "Add to Menu" button, and expand the newly added custom link panel. You'll notice two buttons that will allow you to upload your own social media icons:

As you can see, you can upload a different "On hover" icon that will be displayed on mouseover, and you can select the size of your social icons:

Finally, you'll have to select a position to display the name of each social platform with your icon. If you only want to display the icon without any label, use the "Hide" option:

And that's all ... Simply repeat the above step in order to add all your social channels, and once you are done adding your menu items, don't forget to click the "Save Menu" button ...

OK. Now let's see the live result and some closing thoughts ...