Kyle, great question sir... My situation might be unique as I am an army veteran who has been to Iraq and Afghanistan, and have had training in 2 combat lifesavers courses. The first few minutes involving a trauma victim can be the difference between life and death. Storm chasing is awesome but unfortunately sometimes a tornado hits a populated area and casualties occur. That's when my chasing stops and rendering aid is necessary. I know the professionals are on their way but until then I must do what I can.
First things first, my safety is important. Downed power lines, broken gas lines, fire, and water hazards must be observed. I can't help anyone if I'm electrocuted while standing in a puddle. Broken glass, sharp metal and pieces of wood are also danger items. We call this "situational awareness" in the army. Keep your head on a swivel and be alert/aware of everything in your environment.
Next, I prioritize who needs immediate attention. Stop, look, and listen. There will certainly be others in the impact zone that can help. Organize them into search and rescue teams. They will need leadership and instructions, and many of them may be in shock. Give instruction and they will obey, they want to help too. Listen for cries for help, usually people trapped under collapsed structures or damaged vehicles. Also be aware of tornado shelters that may have the door blocked by debris. Get them out so they can assist in the rescue process.
Locate a safe area where the injured can be brought so that when EMT's arrive they will have a central location for recovery and medical aid. First on the list is airway issues, then bleeding, then fractures, then lacerations. Prioritize the injured. Critical, severe, and then stable is a good way to determine who needs what and when. Those who know CPR should be found and enlisted to provide life saving assistance. If you save one life, you have done your job. I'm also aware I can't save everyone, put those thoughts aside, and do what you can. By the time you have done all these things, firefighters, police, and EMT's will be arriving. At that point, ask them if they require your assistance and do what they ask of you. There really is no better feeling than knowing you have helped others in their time of need.
I prefer tornadoes to occur in open fields of wheat and grass with no livestock in the way. We all know that isn't always the case, so rendering aid to my fellow man is an honor, duty, and challenge for me. Godspeed Kyle, and stay safe sir.