On Insert Trigger To Create Email I am wanting to send an email through the SQL Server Agent once an insert has been made to a specific table.  I tried the syntax below, but the email is not being sent, nor queued to send.  

ALTER TRIGGER [dbo].[Insert_Trigger] ON [dbo].[ProdTable]

AFTER INSERT
AS

BEGIN

EXEC msdb.dbo.sp_send_dbmail  
    @profile_name = 'Test',  
    @recipients = 'XXXX@gmail.com',  
    @body = 'Test',  
    @subject = 'Test' ;


END


If I run the EXEC command by itself in a query window, it executes successfully, so I don't think it's an issue with my general configuration of Database Mail that's causing the problem.

What is the proper way to do this?
Database Mail does not send the mail through SMTP when you call sp_send_dbmail.  The message is put on a service broker queue, and sent by a background process.  

So if the transaction in which the trigger executes is rolled back, then the message will be rolled back from the queue, and the mail will never be sent.  So that's one reason why your mail may not be sent.

Otherwise you can check the log table:

SELECT * FROM msdb.dbo.sysmail_log