U.S. citizens: Students should bring one of the following to their first flight slot following registration:
Non-US citizens: Students should first read the following guide to TSA approval: AOPA.org
When physically present in the USA a student may apply online for TSA approval of training. After students apply (here), the flight school then is able to acknowledge that the student has applied to train at the flight school. Students are then required to pay the $130 application fee. Subsequently an email is sent to the flight school giving the school permission to begin training (30 days max). An email is sent to the student telling them to get fingerprints for the application. The instructions are complex, but in reality the student just needs to get a standard set of fingerprints for a background check from any police station.
The authorization lasts for 12 months maximum. Authorization (and the fee) is required for private, instrument, and multiengine. If any of these courses takes longer then 365 days to complete, they must complete the process (fee, fingerprinting, etc.) again to finish their certification. Example: If the student takes 13 months to get a Private Pilot Certificate, they will have to receive a second approval for the Private and may have to submit another approval a month later before starting the Instrument curriculum. Each approval is only good for 365 days and is curriculum specific.