The fastest way to join a team is using the Team Key, either when creating your account, or afterwards from the Dashboard application. If you are just creating your account and have a Team Key, on the Sign Up page select "I have a team key" and enter the 6 character key provided by your coach.
If you already have an account, visit the Classroom application and, from the Home page you will see an option for joining a team, if you are using your free one account. If you are already part of a team, and want to join another one, visit the Profile Setting page (click on the gear icon from the left) and choose "Join another team".
From the pop-up window, you can select the "I have a team key" option and type in your key to join automatically. If you don't know your team key you can always search for your team (or coach) and send a request to join.
Note: With the Team Key you can instantly join the team, while using request to join will require that you wait for your coach to accept you in the team.