A person can become a better team member in two general ways.

First, people can improve their value to their teams by improving their general level of job skills and their abilities to do various things.  A person who is very technically capable will be of more value to a team than someone who does not know how to do many things.

Second, people can become better team members by improving their skills that are directly related to working with other people.  They can work on becoming better at cooperating with others.  They can work on their communication skills so that they can get their ideas across well and so that they will be better at listening to the ideas of the rest of their team.

In other words, a person can become a better team member by becoming better at working with others and/or by increasing the number of technical skills that he or she has.