Gain confidence through education, experience
ER doctors stay calm while saving lives everyday, and they're able to keep cool by relying on a combination of experience and education. Now, outside of being that guy in Catch Me If You Can and impersonating a doctor to gain some life-saving experience, first aid training will suffice.
Dr. Stanton put said experience to work one Sunday outside of the ER, when someone passed out behind him in church. While other people were freaking out, Dr. Stanton followed his own advice and everything turned out fine.
Other, non-passed out churchgoers were concerned that the unconscious person didn't have a strong pulse, and that it was imperative to check their sugar. But Dr. S knew the best move in this situation -- make sure the victim was breathing and stay there until EMS arrived. And to stay calm. In a hospital, "if the doctor is calm and relaxed, the whole [ER] is calm and relaxed and everyone does their job." Be the calm one in any life-threatening situation you encounter, and you'll do just fine.