This is a great question. And cobaltduck gave a great answer.
I teach martial arts, and often the way we teach to calm the mind is by controlling the breathing. Meditation is always the answer: nothing is gained by panicking. We have many sayings in life, like "Look before you leap", "Think before you do", etc. And that's easy to say, not so easy to do. For many, the problem is exacerbated by the snake itself - venomous or not. Ophidiophobia is one's worst enemy.
Having said that, breathing calmly and not thinking bad thoughts is a learned and practiced skill: you can't expect someone with no practice to do just that. Therefore, in your first aid classes (we outdoors people DO study first aid, right? ;-) part of your practice on tying square knots, splinting broken limbs, stopping bleeding, and starting breathing and hearts, should also include exercises in breathing exercises.
Those who are in traditional martial arts, or who take yoga, or otherwise are well-practiced in Asian healing are usually good resources.
In short, you will want to settle down as quickly as possible. Drink nothing but water - caffeine, for example, will increase your heart rate, you don't want that. Slowly breathe in and slowly breathe out - all at the same slow pace. You should not assist in your first aid, unless you are alone or the others are panicking or don't know what they're doing. The more you move, the less you can focus and reduce your heartrate.
One thing you might want to focus on is the snake. Good first aid dictates that getting a picture of the snake will be important for medics to prescribe the proper antivenom. But if there is no camera, you'll have to keep a mental picture of the snake. So, look at it, verbalize what you see: the rattle, shape of the head, its length, its colors, and every detail you can see about it. Of course, if the snake is dead or gone, you should focus your efforts on other things, like the serenity of a blue sky, or an ocean sunset. Maybe try to count the different kinds of birdsong you hear, or count the number of animal life about you. (And while your at it, if others are in a calm mind, they should also snap pictures or verbalize what they see as well).
Again, this good advice - but useless if you don't have the practice. Take up yoga, martial arts, qigong. Or just practice meditating on your own.