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 Dashboard application and click on the user profile picture (upper right side) to open the user menu, and select "Join a team".
From the pop-up window, select the "Yes, I have a team key" option and type in your key. 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.