Hello Alli Renshaw,
As Christine already says, instructors can be either employee or independent contractor. In either case, you want to keep a log with proof of certification and expiration dates. Then have the trainers present their card for you to make a copy and keep in your log/file.
Natalie aka NAPS 2 B Fit.
I am assuming you would be referring to a certified group instructor. Certified Group Fitness Instructors are usually issued a card or certificate that indicates their certification expiration date as well as what particular specialty it is. Each certifying agency is different, but there are continuing education requirements instructors must fulfill in order to be re-certified (they include online tests, workshops, classes, etc.). That would cover their part of the required education needed to re-certify with a particular agency. You can hold them accountable by requiring them to submit a copy of their card and renewal cards when they re-certify. You may have your own requirements as well.
Instructors can be either an employee of the gym/facility or they can be independent contractors and carry their own insurance.
Hope this helps answer your question.