Note that there are spoilers below, so read at your own risk.
1. Focus on solving the problems.
This is the underlying theme of the entire movie. It would have been extremely easy for Damon's character, Mark Whatney, to sit down and die, to give up. Instead, he spent his time solving his problems, on moving forward.
2. Solve one problem at a time.
At the end of the movie, Whatney is giving a speech to a class of astronaut wannabes and he tells them that for their entire lives, they will be faced with problem after problem. He tells them all they can do is go to work on the first one, solve it, and then move on to the next problem. On this list, #2 is the key to #1 -- realizing that we can't solve all of our problems at once and focusing on the most important one before moving on to the next oen.
3. Don’t take yourself too seriously.
Mark Whatney jokes at every turn. When he nearly blow himself up, he jokes. When he is about to try something that could easily kill him - such as puncturing his suit in space so the escaping air will propel him like a jet blast -- he jokes.
4. Make jokes.
I suppose #4 is pretty much the same as #3, but the Damon character really does joke a lot. Above, we see him joking in the face of crises. But he also jokes about the successes, such as when he He literally integrates humor into every aspect of his life. This absolutely must be a key to his happiness and to his ability to succeed.
5. Take your victories where you can get them.
Mark Whatney knew that there was nobody else to motivate him, and it was totally up to him to keep up his personal energy. He celebrated every little victory, knowing that they were important steps to reaching his final goal. He got excited when he figured out how to grow potatoes; when he discovered how to stretch his battery life and go longer distances in his electric vehicle; and when he learned how to communicate Earth.
6. Move through the tough parts as quickly as you can.
One of Whatney's very first challenges was treating an injury. There are people in this world who could not have pulled a long piece of metal out of their belly, nor stapled the wound closed without any anesthetic. These things were incredibly painful, but Whatney knew they had to be done quickly or he would die. So he did them, and he survived.
7. Don’t dwell on things.
Over and over again, Whatney had setbacks -- from losing his potato crop to the entire situation of getting stranded on Mars. He never dwelled on the problems; he focused on solving them and moving forward.
8. Communicate.
Whatney communicated about absolutely everything, taking videos and sharing them with his team back on Earth. This helped him keep his spirits up, made him feel less alone, helped him think through and solve his problems, and even allowed them to come to his aid. When it gets down to it, communication can make most things better.
9. Analyze your situation.
As a scientist, Whatney was great at analyzing his situation and then moving toward a solution. Too often, we see a problem and immediately decide it can't be solved. The fact is, that there are very few problems that cannot be solved, or at least made better, if we take the time to think them through.
10. Take calculated risks.
One of the great scenes in The Martian is when Whatney takes off into space with nothing but a tarp covering the nose of his rocket (because he need to make his ship much lighter). This sounds a little nuts, but was scientifically sound, and allowed him to leave Mars. Taking a calculated risk made all the difference.
If you haven't, go see the movie. It is so much fun, and offers important commentary on dealing with the troubles life throws at us all.
