For any team to be successful, everyone has to be working toward the same vision. The entire team needs to clearly understand the vision and be motivated to get there. Do Your Part - On successful teams, every member of the team does their job the best that they can - every time. They work hard consistently because they have a desire for the team to succeed and they understand their role and feel appreciated.
Pep Talks - Teamwork requires constant motivation. Great coaches give "pep talks" more than once a year, but before every game, at time outs, half-time and when the game is over (win or lose). Motivational talks are given at practices and team meetings too.
Stay Positive - Teamwork also requires feedback on performance. Most leaders, including myself, tend to concentrate on giving negative feedback, correcting mistakes. That is necessary, but I find it to be most effective when I concentrate on giving positive feedback, congratulations and gratitude for outstanding work. Try to give three positive comments on performance for every correcting comment. It is important not to get caught up in how often "reviews" are given. But have a habit of saying "thank you" and "great job."
Trust - True teamwork is achieved when everyone on the team trusts that everyone is doing their job. Trust comes from faith in each other that can grow, with time, into a strong comradery that is felt among the team.