The most vital part of being a great team member is being selfless. It is important that you put the team goals ahead of your own personal goals. Cooperate with your teammates instead of competing with them. If you are done with your work, ask to see if there is more work that you can do or try to assist the team members who have not finished their work yet.
Being a great team member means being honest with yourself and your teammates. If you need help, don't be afraid to ask your fellow team members for help, they'll more than likely be willing to help. If you are given a task that you don't know how to do or believe that you can't finish on time speak up and let your team leader know. If you make a mistake, admit that it was your fault, in the long run you'll earn a reputation for being honest and you'll earn the trust of your teammates.
It is important that you are respectful to others on your team. Being polite to your teammates is important, a simple "thank you" or "please" can mean a lot. Take the time to listen to your teammates and give constructive feedback whenever the opportunity arises. If you see a problem within your team, don't just complain about it or place blame on others; instead, come up with a resolution to fix the problem.
Being recognized as a great team member doesn't happen overnight, but if you are persistent in striving towards becoming a selfless, honest and respectful team member, you will win the respect of your teammates.