How do I approve and promote members?

Manage → Members. Pending requests are accepted or declined there, and you can change any member's role — promoting a trusted member to moderator is how you stop being the only person handling reports.

Two limits are deliberate: the owner cannot be removed or banned by anyone, and an admin cannot remove, ban or outrank another admin. Only the owner can do that, so a club cannot be taken over by someone you promoted.