The answers for a psychiatrist differ from a psychologist.

Psychiatrist

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.

Psychologists

American Psychological Association article on Forensic Psychology.

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.