Adding an icon in WordPress is easy with the plugin called Menu Icons.
First, install and activate this plugin, then you are ready to add the icons.

Adding Icon
Create a new menu throughAppearance > Menus.
Don’t forget: assign the menu location, otherwise it will not show up anywhere in the website.
Then you add an icon for each menu item.
To begin, let’s expand one of the menu items.
You will find alink "Icon": Select icon.
Click on the “Select icon” to start the selection.
Here you will be finding awindow similar to the media library.

At the time of this writing (January 2016),this plugin has 3 font icon libraries:
Dashicons, Genericons, and FontAwesome.
It is better to only use 1 of them.
Reason: They all have their specific traits like size and curve for example and it is better to just use 1 kind of an icon on your site.

If you use FontAwesome, use it on your complete website. It will give your site a more professional look.
When you select the icon, you will see the preview on the right panel.
In the right panel you can make some adjustments.

You canplace the icon before or after the menu, control the font size, and set the vertical alignment.
When the setting is done, clickon the Select, and proceed to add an icon for the other items in the menu.