You will be credited $5 when someone clicks the referral ad from your site and signs up for Google Apps with a domain that has not already been signed up for the service. That person's domain must then have one or more Google Apps email accounts in use for four consecutive weeks. It's that simple.
There is no mention about whether this is the premier edition of Google Apps but I would imagine that this would be the case.
It appears from the forum discussion that this is only available to subscribers in the United States.
If you do have it, it should look like this:
Google Apps has also added a page in their Help Center that describes the process.