First and foremost when it comes to protecting your gym or PT studio/business, speaking with a lawyer in the jurisdiction where your business is located is best. That way they can advise you of the specifics, if any, are needed to be placed in a member agreement/contract.
I am a gym owner and not only do I place safety notices in the membership agreement, I also have the member go through the gym with a staff member at orientation and demonstrate to them safety issues with equipment, their responsibility of re-racking the equipments and their part in equipment cleanliness (using a towel & wiping down equipment after use). I also place in the safety notices where emergency features are located, request their respect toward other members and staff and notify them that inappropriate behaviors will not be tolerated. Additionally, age requirements are noted.
I hope this is at least a helpful start. If you have any specific questions, I would be happy to answer them to the best of my ability and expertise.
For more Gym Business Insights, I have a blog that you can visit that will also help out with issues that gym owners deal with.