We can configure alerts for database mirroring by many ways. Generally when mirroring fails like mirror server is down or principal server is down in opposite partner we will get 1474 error.
We can configure event alert for this error we can mention some operator name in alert response. But before this you have to configure Database Mail. You can check the following link to configure database mail.
Configuring Database Mail in SQL Server
We can configure WMI Alert also which sends the notification to required EMail ID.
Hope I have answered your question.