I’m afraid that explaining how to use software that has nothing to do with Discourse is usually out of the scope of this forum. If you have trouble and a budget, you can post in Marketplace. 
That said, I agree with pfaffman, likely Mailgun wasn’t properly configured (many people use it for Discourse with no troubles) or app.yml wasn’t properly filled in. I’d look at both, and as for changing SMTP settings, as pfaffman said a few times, you can also run ./discourse-setup, which will lead to the software’s configuration step by step.