Go to League-Systems.com and click on Find league. Then find the league you want to connect to and click Apply. There you can then choose to connect to a team.
When you submit the application, you will not be directly connected to the team. You end up in a queue list of the administrator who is then responsible for adding you to the team, if approved.
If you need to get in touch with the administrator to check the status, you can again find the league and then click on the Start menu. There you see who is the administrator and if you click on that person, you can also send a message directly from the system.