Both supervisors and workers must follow any relevant policies, procedures and safety requirements with a focus on best safety practices.
The first point of responsibility for safety lies with the supervisor. In the case of research labs this is usually the principle investigator. Read the supervisor's handbook.
You must make sure workers are adequately trained in new tasks before they do them. The expectation for training includes the worker successfully demonstrating how to do new tasks and following prodecures safely. OHSE provides training to augment the lab specific training and standard operating procedures you provide.
Workers and students
You are expected to take personal responsibility for your own safety and not endanger others. This includes having knowledge and training about risks, protective equipment, best practices and reporting any safety incidents or concerns. If in doubt, ask before you act. Read the safety handbook.