1. Proper Attire. Proper attire is needed not only to keep you comfortable but also to keep the upholstery on the machines in good condition and keep you safe. Some fabrics, especially those in jeans, are abrasive and can cause the material on benches to rip. One of the most important rules to follow at the gym is wearing the right kind of shoes. Any athletic shoes will do. They'll give you the right grip so you won't slip and they'll protect your feet incase you drop weights.
2. Bring a Workout Towel. Everyone sweats during a workout and wiping it off is important in keeping the gym as clean as possible. Most gyms provide disinfectants to use on machines if you've sweated excessively. Leaving a machine sweaty after you used it is rude and very unsanitary. It can spread germs and get lots of people sick. While most gyms don't require it, bringing a towel of your own is a good idea.
3. No Gum. You should not chew gum at the gym. While no one purposely spits it out, you can accidentally drop and create a mess. While working out, you might also accidentally swallow it or let it go down your air pipe which could create a safety hazard.
4. Sports Bottle. Getting thirsty is a normal part of working out. If you want to bring a drink to the gym, make sure its in a sports bottle that has a cap on it. A cup could lead to spills which can cause accidents.
5. Allow Work Ins. A gym is a place where everyone can workout. If you are working on a machine and someone asks to work in, allow them to do so. While you rest, the other person can finish a set with very little work needed on your part. Free weights are a bit different since changing a lot of weight can be difficult if neither of you are in the same weight range.