On more than one occasion I have found a highly-excited victim, looking very pale and washed-out, breathing at twice the normal rate (12 to 20 per minute) and presenting with an elevated pulse rate (over 100 beats per minute). By simply talking calmly to the individual as I assessed her condition, I was able to bring her down to more acceptable levels.
So how does one remain calm? The first rule is to take a deep breath and slow-w-w down. In emergency medical services we say SLOW IS FAST! The next time you see fire/rescue or the ambulance come to your neighborhood, watch how the first responders deploy. It's not likely you will see them running blindly onto the scene. Their actions will appear to be deliberate. Many will take a "gutter gaze," in other words a good look around the scene to be sure it is safe before rushing in. Once the scene is deemed safe, they will calmly unload the appropriate equipment and WALK to the victim. Rushing into an emergency almost guarantees that you will bring the wrong equipment, go to the wrong location, do the wrong thing or trip over each other. It's much better to just take a deep breath and begin your protocols.
Even when you have no equipment or supplies, your voice and your calmness can go long way to stabilizing the victim and leading to a successful rescue.