The amygdala is one of the most interconnected parts of the brain, it is highly involved in the fear response, but due to evolution the neocortex has also become involved. The frontal lobes of the neocortex are located just above the eyes. They process conscious, rational thoughts and give us our most human-like qualities. Information from our senses reaches the amygdala almost twice as fast as the frontal lobes.
Here's a bunch of techniques from a documentary that showed SEAL training.
Goal setting: concentrating on specific goals lets the brain brain bring structure to chaos. This reduces arousal of the amygdala.
Mental rehearsal / visualisation: continually running through an activity in your mind. This allows the activity to flow more naturally when performed in real life. By practising in your mind first, whenever you experience the event for the first time in real life it is actually the second time that you have encountered it. This means that the event causes less of a stressful reaction.
Self-talk: this helps focus your thoughts. The average person speaks to themselves at a rate of 300-1000 words per minute. If these words are positive (embodying a can-do attitude) as opposed to negative (can't-do) then they will help override the amygdala's fear response.
Arousal control: by breathing in a slow, deliberate manner we can reduce some effects of panic. Long exhales in particular have been shown to calm people down in times of heightened emotionality.
These are some of doubtless many techniques which are used by the military to promote mental toughness and persistence.