This article is from the Aerobics Fitness FAQ, by firstname.lastname@example.org (Robles) with numerous contributions by others.
Currently, there is no license (as in a medical license) required to
be an Aerobics Instructor or Personal Trainer. Periodically
legislation is drafted, but the industry has done a remarkably good
job of policing itself.
While most clubs require certifications of their instructors, there
is no law against teaching without a certification.