While the above is the correct approach, if you are in need of some comic relief or small injection of humor....there are other tactics which work just as well but are not typically taught in school.
One of my favorites, which is successful due to human nature/psychology.
People freak out because they are no longer in control. It is an unfamiliar situation and they do not know a proper response to feel helpful. This is why the medical team by staying calm and issuing tasks can control the scene and bring calm to the person by sending them on tasks.
You also have to know your audience. For example, typically a young teen is not on medications. So if you say go search for them the grandmother may reply quickly she doesn't take any and you have not solved your issue. same with insurance card...it may be produced or denied as having almost immediately.
I like to send them searching for more obscure objects...for example...calmly direct them to go find you a pink highlighter...or maybe a green one. Say the command with enough authority so they do not doubt your seriousness.
They will immediately seize this mission and go searching. This search can buy you several minutes of needed silence or no interference. Typically people do not have pink or green highlighters just laying around.
When you ask the person to do this, they never question why you want one, they are just happy you have issued a task and they have something to do.
Try it...it really does work.