This is my general methodology:
Set up the alert so that it fires to the Alert Monitor - this is wholly within Splunk, so it will tell you whether your search is correct and the alert mechanism is working properly. Once you have the alert firing, only then enable your email connection.
The email connection is done by setting Manager -> System Settings -> Email Alert Settings. It's an SMTP server. The best method of testing this is by using telnet to port 25. In many organizations, you will also need to configure the SMTP server to allow connections via SMTP from the Splunk server. By testing the connectivity outside of Splunk, you ensure you have the settings correct.
Finally, check the logs. do a search index=_internal and look for errors related to email. You will generally see the server name or email address you entered in the error message. This will enable you to narrow down the specific reason that email is failing. Things that have a 550 code in them are produced by the email server (not Splunk) and generally indicate a configuration problem.
