At the risk of promoting more spam, I'd suggest:
1. Use the mail command to confirm that sendmail is or is not properly set up.
echo "this is just a test" | mail -s "test message" firstname.lastname@example.org
This sends an email to your own external email address. Give it a few minutes, then type in 'mail' on your Linux server to see if there is a bounce message. There probably will be. Type 'x' to get out of the mail client (and retain read messages) or 'q' to quit (and delete read messages).
2. Google for "configure sendmail".
Why reinvent the wheel here? The first one I looked at, http://www.wikihow.com/Configure-Sendmail
, looks promising, but I've I've spent hours arguing with/configuring 'sendmail'. Eric Allman's book was authorative at one time. I don't know if it's been kept current.
3. Use #1 to test it, once you have it configured.
(Make sure you 'su' to the same id that is sending the mail before you use the 'mail' command to look at responses.)
As I said in an earlier post, sendmail is not easy to configure. The catch that I see here is that you may need to relay mail to a server that can establish post 25 connections to your mail destinations. The bounce messages will be informative.
I really can't contribute much more than what I already have.