Contact the hospital or other facility where the x-rays were taken. Information on how to access your records should have been provided to you at the time of the procedure pursuant to HIPAA.
Find out what the procedure is at a particular facility to get possession of an x-ray. Some hospitals will take your name and birth date over the phone and have the x-ray ready when you arrive. Then you will have to provide personal information, probably a photo I.D., and sign a form.
Request in writing that your x-rays be provided to a third party if that is your wish.
Be prepared to pay a reasonable fee if you intend to keep the x-ray. Most hospitals or doctor's offices will ask that you return them for safekeeping with the assurance that you always have access to them. Also, you will probably be asked why you want the x-rays. For instance, they may want to know which doctor is requesting them.
File a complaint with the U.S. Dept. of Health and Human Service's Office of Civil Rights if you are unable to get possession of your x-rays (see Resources). You may also be able to file a complaint with your state.