This post is for those not in emergency services. This is what to do when you are confronted by an emergency. Just a down and dirty way to help someone that needs you. This should not take the place of a first aid and/or CPR courses
First and foremost, when an emergency presents itself, stay calm. I understand that this is easier for some people than others. Take a second and plan your course of action. Then do it. Now for what to do.
We'll start with the bad one. If someone collapses unconscious in front of you, call 911. Then check for a pulse! Don't worry. If you forget what to do the 911 dispatcher will be able to walk you through it. If there is a pulse, keep checking on it and wait for the cavalry. If there is no pulse, start just compressions. If you don't want to then at the very least do compressions in the middle of their chest like you've seen on TV. Do compressions fast and hard. Keep going until trained personnel show up. If there is an AED grab it and follow the simple directions on the machine.
Severe bleeding. I would think that a lot of blood would freak a lot of people out. The first thing you should do is call 911. Then use something (preferably clean) like a towel or shirt and apply pressure directly on the bleed. This may hurt but it should stop the bleeding. If direct pressure doesn't stop it then apply a tourniquet above the wound. Get creative. Use a belt or something else that you can tighten to cut off blood flow.
Poisoning. Call 911 then call poison control. Follow their instructions. Even as a medic I still call them when my patients have overdosed on something with which I am not familiar.
If you have a fire, get out and call 911 from somewhere safe. Do not go back in to a burning building. All you'll end up doing is giving us someone else to rescue.
If you happen across a vehicle accident and people are injured. Call 911. The best thing for you to do is to stay safely belted in your vehicle. Roadways are among the most dangerous places that emergency service personnel have to function. Without proper training you would probably be putting yourself at great risk. If you do decide to stop, don't move someone from the vehicle unless it's on fire or going to fall off a cliff.
Basically, stay calm, call 911. They'll talk you through what you need to do. Just don't be afraid to help out.