Our first step is to setup Mail Exchanger records - commonly known as "MX Records":
http://en.wikipedia.org/wiki/MX_Records
An MX record tells a sending email server that Mailgun is accepting email for your domain so it gets routed appropriately.
To setup our MX records, make sure you are logged into DigitalOcean, and go to the DNS records listing for your new domain (DNS -> click on the magnifying glass to the right of your domain).
Next, click on the big blue "Add Record" button in the upper right corner, and choose "MX" as the record type: