You send a form with copies of your licenses to the FAA.
They send a request to the Canadian authorities, they go through their files and confirm/verify/authenticate you hold a license.
That is called the "letter of verification".
With this letter you go to a regional FAA office (FSDO) of your choice to show/ID yourself and they type out your "restricted license based on foreign license" which is only good for private priviliges.
You can read about it here also:
http://www.eaa-fly.com/2.0/en/MainTr...ertierung.html
If you wish to fly as a Commercial Pilot in the US you need to take the appropriate written tests and check rides w/examiner.