In the lab? PPE like a fume hood, gloves, goggles are standard. In special situations other precautions may be warranted, such as blast shield, face shield, respirator, and so on. It depends on the chemical and process. In practice, universities do not often enforce safety standards (or they do so only in a token way - like a yearly 1 hour seminar). This may slowly change in the wake of what has happened with Patrick Harran of UCLA. (http://blog.chembark.com/2014/06/22/ucla-professor-patrick-harran-strikes-deal-with-prosecutors/
) Let's hope so. It's amazing more graduate students aren't injured in the lab at Universities.
In the plant, usually regulatory agencies (at least in the US) like OSHA establish safety guidelines and conduct inspections to make sure they are being followed. Most chemicals have set exposure levels. These rules definitely are usually followed because of the severe penalties for noncompliance (financial and criminal).