The first thing to do is to apply to have your foreign certificate verified by the FAA. Visit the FAA Airman Certification website and follow the directions on that page. When asked which FSDO you will be visiting, indicate Scottsdale, AZ. Submit the application and attachments by mail, fax, or email.
Next, you will be sent a LETTER OF AUTHENTICITY from the FAA, which you must bring to the U.S. with you. A duplicate of this letter will also be sent to the Scottsdale FSDO as the letters will be matched up when you arrive. The FAA says to allow at least 90 days for the letter to come. It usually takes a lot less time, but plan ahead. We are able to call the FSDO and check if your letter has arrived in case you wish to know. Do not call before your letter comes to you.
With proper documentation you simply go to a Federal Aviation Administration (FAA) Flight Standards District Office (FSDO) and they will issue you a U.S. Private Pilot certificate with the ratings and limitations as shown on your country’s certificate. You then go to a flight school and complete a U.S. Flight Review, which includes ground training and flight training. This is usually done in one ground training session and one flight for current pilots. The Flight Review is good for two years. At Chandler Air Service this also meets the requirements for a checkout to rent an airplane.
Upon your arrival you’ll need to set the appointment and go to the Scottsdale FSDO to have the certificate issued. However, be aware, they do not do this on the weekends. If your schedule is tight, you can set the meeting in advance. You do not need the license to do the Flight Review and checkout. You will need it before you can go solo or PIC (Pilot In Command).
It is quite normal to fly upon arrival, and get the certificate issued in the next day or so. The FSDO office has no way of tracking your incoming letter. They only know when it arrives. There is a process on the FAA website to check the status of your letter.