How do you motivate people?

What’s the biggest motivator? Progress.

Via The Progress Principle: Using Small Wins to Ignite Joy, Engagement, and Creativity at Work:
Of all the positive events that influence inner work life, the single most powerful is progress in meaningful work; of all the negative events, the single most powerful is the opposite of progress—setbacks in the work. We consider this to be a fundamental management principle: facilitating progress is the most effective way for managers to influence inner work life.

What’s the right attitude for A leader to have?

The best leaders are supportive, not controlling, even in the military:
Via The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work:
In the U.S. Navy, researchers found, annual prizes for efficiency and preparedness are far more frequently awarded to squadrons whose commanding officers are openly encouraging. On the other hand, the squadrons receiving the lowest marks in performance are generally led by commanders with a negative, controlling, and aloof demeanor.

Want your employees to perform better? It can be as easy as believing they are smarter than average and having high expectations. (Expecting people to be selfish can be a self-fulfilling prophecy.)

How can you inspire people?

Remind them why their jobs are important.
Noah Goldstein, co-author of Yes!: 50 Scientifically Proven Ways to Be Persuasive, reviews a study:
Adam Grant, a scholar in the field of organizational behavior, realized that workers often fail to live up to their potential because they’ve lost track of the significance and meaningfulness of their own jobs. He figured that if he could remind employees of why their jobs are important, they might become more highly motivated, and therefore, more productive individuals.

What magic do both the speeches of Martin Luther King and the marketing of Apple have that move us to believe and act?

Simon Sinek, author of Start with Why: How Great Leaders Inspire Everyone to Take Action, has an interesting theory:
People don’t buy what you do. They buy why you do it… Start with “Why.”