Let me implore you. If the area isn't safe, do not even attempt to enter the scene. Fires can instantly flare up and engulf a room in seconds. Rivers can be so cold they cause shock upon entering the water and, in some cases, they cause cardiac arrest. Tiny pieces of broken glass can cause deep, sometimes life-threatening lacerations. An accident on the side of the road can immediately escalate into a multi-vehicle incident if another driver doesn't pay attention.
What we don't want to happen is for you, the hero, to become another patient. Not only are you putting your life in danger, you're also increasing the risk for your rescuers as well.
What you can do is this:
1. Secure the scene. If the accident occurred at the side of the road, park behind the accident and turn your hazards on. Wave at traffic to slow down and be cautious around the accident. If there is a house fire, try to find the gas shut-off valve and turn it off.
2. Assist the location of the scene. It's often difficult for EMS to locate the scene of the emergency. Standing near the front of the building or the entrance to the parking lot and flagging the ambulance/PD/fire down helps a ton. Leading them directly to the scene is just as important.
3. Use your common sense. Don't let the panic take hold of you. Be rational, reasonable. I'm not saying you should never try to help someone, just make sure that YOU are safe FIRST before heading in to assist.
I hold EMT/Paramedic certs and volunteer in my spare time.
Thanks.
Edit: I also want to point out that there is generally very little anyone can do aside from basic management of the ABC's (airway, breathing and circulation) without equipment. Some of that equipment is located onboard a fire truck or an ambulance. Most of that equipment is usually found inside the operating room of your local hospital. The faster the patient is moved safely to the local ED, the better it is.