"You saved me tons of work"
— Tanner Moushey What They Say

How can I change the number of posts (or sermons, events, etc.) shown per page?

You can change the number of entries shown per page in Settings > Reading with “Blog pages show at most”. This affects all post types (blog, sermons, events, people, locations), not only blog posts.

If you want to change the “per page” setting on a per post type basis (ie. show 5 sermons per page, 12 events, 10 blog posts, etc.), try the Custom Posts Per Page plugin.