Choosing an icon
To use Font Awesome in Moodle you can just add a simple code in the HTML view.
For example, if you want a Moodle type graduation cap icon, you can add:
<i class="fa fa-graduation-cap fa-5x"></i>
So, you basically enter a small string of text in HTML view that inserts an icon into Moodle. There are thousands of icons to choose from. Easiest way to try? Create a new Label in your Moodle course, and in the editor HTML view, try adding this code (you can copy and paste if you want) and save to see what you get:
<i class="fa fa-apple fa-5x"></i> <i class="fa fa-facebook fa-5x"></i> <i class="fa fa-twitter fa-5x"></i>
Those of you with some basic HTML knowledge will recognise the <i> tag, which means italic. In reality most web designers use <em> (for emphasis) to display italic text, so it's OK to use this (and is recommended on the Font Awesome website).
Or use a span if you want to be more correct, which I like to do:
<span class="fa fa-apple fa-5x"></span>
All good ?