This is one of the most asked questions I receive as a sport psych coach, and believe it or not, it's one of the most difficult to answer. The main reason? No two people are motivated by exactly the same thing. Most coaches/teachers/parents have heard of Intrinsic and Extrinsic Motivation, but effectively implementing one or the other can be a frustrating challenge for everyone involved.
Extrinsic Motivation tends to get a bad rap due to the focus centering on performance outcomes rather than the performance process itself. In other words, if you perform well - you get a trophy and more starting time; if you play poorly - you will sit the bench. Athletes that strive to play their hardest for the accolades of success can have a steep drop-off in motivation should they lose or 'fail' in competition. That being said, I have worked with a number of athletes who seem to excel with this 'reward/punishment' system. They spend time working out and training not because they enjoy it, but because they know they will get compliments from their coach and it will help them perform better on the field. For these individuals, the added performance anxiety is manageable and intentionally used as fuel to work harder.
Intrinsic Motivation is what most high level athletes possess an abundance of. They thrive in the process of performing and are more able to have a big-picture view of their growth and progress. While these athletes or students are more steady in their motivation, they can lack the burst of motivation that pushes individuals to their limit - think of the baseball team whose coach just said he'll buy them all ice cream if they win their next game. Intrinsically motivated athletes generally aren't afraid of making mistakes and possess more conviction in their ability.
Bottom line: To motivate an individual successfully, you need to find the thing that motivates them the most. Why are they playing their sport/taking their class/doing this activity? It is imperative that you reach them on a personal level and demonstrate that you aren't just interacting with them as a job/because you have to, but instead because you're truly invested in them and their success. Assert that it's ok to make mistakes AND actually practice this philosophy (allow them to maintain their position after a few mistakes while demonstrating how they can learn from them). Lastly, don't be afraid to throw in a reward here and there for work well done!