Basically you need to forward the email twice. The first time from dreamhost mail system to the webserver. Then on the webserver forward the email to a pipe.
For the first step log into the dreamhost panel and choose Mail > Message Filters. Click edit next to the email account that will be receiving the email, on the next screen add new filter. You want the option to "Forward to a Shell account", and the possible options should be presented for you in a dropdown list. Your dedicated server user should appear in the drop down list.
Note: to forward "ALL" in the above step, the simplest way is to use reverse logic with a garbage string i.e. "Subject does NOT contain "dklfjdkfjdfkjdkjf"
Now the email will be forwarded from dreamhost's mail servers to your webserver's user, once it's there we need to forward to a script on the webserver using a pipe. See this wiki article for examples: http://wiki.dreamhost.com/Email_to_Script
no cron needed.