I just went through this process not to long ago.

One, you need to be able to fly high speed aircraft, and demonstrate that to two people approved by the AMA. Usually CD's in your area. There is lots of leeway in how you accomplish this, and its mostly up to the CD's. I accomplished mine by flying a pattern plane that was setup for higher speed, as well as having the CD's seen many years of my flying many other airplanes both high speed and complex.

I had to go through a ground school to show that I knew how to operate the turbine safely, perform emergency shut downs, normal starts, handle hot starts, etc. The ground school also covered the requirements and differences you will encounter with turbine powered airplanes such as residual thrust issues, safety issues, etc.

The above generates some paperwork, and that would need to be turned in to the AMA. Sometime thereafter, you will receive a waiver. The waiver is your 'permission' slip to be shown to the contest directors at any AMA event that you wish to fly in. It basically tells the contest director, or local club official, that you have passed the requirements set forth by the AMA for turbine operation, and that you are allowed and covered under the AMA insurance program to fly turbines.

I'm sure others will go into more detail for you. But thats the process in a nutshell. Its not hard if you just take the time to do some studying, which is what its all about. The turbines are more complex than prop engines, and have special needs and considerations. The AMA just wants to make sure you are well aware of them, can handle the responsibility to operate them safely, and can handle the aircraft in the higher speed envelope. Saves the AMA from having to insure those with an abundance of self confidence and cash coupled with less than a normal amount of common sense and restraint.