Anyone may create a tournament. A club is different: it keeps running, it has members, and its standings span seasons. That is why creating clubs is not open by default.
Click My club at the top. If you do not have access yet, you will see a form: state which club you want it for and what for. Your request goes to the administrator and you immediately get a confirmation e-mail. Once it has been handled you will hear by e-mail — on approval, with a link to get started.
While your request is pending you will see it in the same place. You can only have one at a time.
Existing clubs are always kept and remain manageable. Access only concerns creating new clubs.
To let someone help with a club that already exists, that person does not need to request anything. Add them under Managers in the club management and tick which parts they may see. A free account is all they need.