The lab environment is hazardous by nature. The actual risk is largely determined by you and those working with you. It's your responsibility to know and follow the rules and be able to recognize potential safety hazards.
The first consideration is proper dress. What you wear in the lab can help prevent serious, even fatal injuries.
Often, you'll be working with chemicals that could harm you if they come into contact with your skin. That's why you need PPE - Personal Protective Equipment. For general lab work, a lab coat, safety glasses or goggles, and gloves are required.