Here's a good howto on incoming mail processing. The simplese thing to do is to use the .forward mechanism as described, to pipe a message through a script. Create a mode 600 .forward file in the user's home directory and put a pipe to a script in it:
"|$HOME/bin/your.program -and some arguments"
However, you should look at using procmail instead, as that howto details. Procmail gives you a lot of advantages, such as more sophisticated logging and mail processing. Here's a simple .procmailrc example (again from that same howto):
:0
* !^FROM_DAEMON
* !^FROM_MAILER
* !^X-Loop: myaddress@myhost.mydomain.org
| $HOME/bin/my.script
which has some nice features, like the ability to detect and stop mail loops.