How do I become a Forensic Psychiatrist or Psychologist?
The answers for a psychiatrist differ from a psychologist.
A fellowship is the first step for a psychiatrist. Fellowship is a one-year program that follows Psychiatry Residency. Fellowships are only offered at a few dozen schools in the US. Information about Fellowships is available from the American Academy of Psychiatry and the Law site (AAPL).
The American Board of Medical Specialties
Board-Certification in Forensic Psychiatry–or any specialty, is granted by the American Board of Psychiatry and Neurology. The American Board of Medical Specialties publishes a report of both Board-Certifications and requirements. Cross-specializations are sometimes attainable as valuable complement to Forensic Psychiatry. Read the 2018-2019 ABMS report for more information.
For a psychologist the range covers postgraduate study, APA Board-Certification required training, fellowships, internships, Masters Degrees in Forensic Psychology certification programs, and it goes on. Specific colleges and universities offer degree programs in Forensic Psychology.
Many other sites do a better job of answering this question than me so I will leave it to them. It isn’t my area of knowledge.