Is it possible to motivate people (teammates) at work as the Team leader? If yes, then how? If no, then why? or Are people self-motivated?

YES : you have to be a strong leader and to give people both individual attention and to recognize them as a team. Whether you're the CEO of a company or the leader  of your department, there are many things you can do to get the people around you motivated through good behavior and need to tell company needed new goal on every month so our company will bright as well benefit will comes to us through yearly bonus or increment if we given relevant performance. 

Being a team leader is a responsibility and a leadership quality person can do it. In most of the teams, people want to be a team leader, but they do not that how to manage the team. For this motivation, proper training, each employee having proper JD's will generate a leader among the team. 

Sure there is many way to motivate teammates :

1- Giving clear training 

2- understand every employee learning style 

3- coaching 

4- set a clear job description 

5- Follow up (Take the soft approach ) 

6- create a challenge and set clear objective for the team 

7- give feedback ( positive or corrective ) 

8- explain if it was negative or positive ( why )