Under Settings, you can connect Audience to Mailgun, AWS SES or Sendgrid to send your emails.
To connect Audience to Mailgun you will need to set the domain and API Key from your Mailgun account. Set the API URL to the right API for your Mailgun domain.
Once you enter your details and click Save Settings. Audience will send a verification email using those settings.
If the email sends successfully you will need to click the "activate email" button in the email to enable your email provider in Audience.
If the email fails, it will report that in the screen along with any message from your email provider.