First, go to the Tournaments section to choose the tournament.
Set the type of the tournament, control, date etc. According to your preferences. Let’s say we’d like to play a Swiss system tournament on 12th of December with no entry fee and we do not mind the control.
Arena will suggest you a tournament. Click on it and then on the "Join" button. You will be notified by email 30 minutes before the tournament starts.
If you can't join a tournament, it might be that the maximum number of participants has already registered, or the tournament is being held for a specific group (groups can be specified by rating or region).