How do I delete a genre?

There is a switch under the settings page called "Predefined Genres" that when set to OFF will remove the pre-populated genres from being displayed as a selection (unless that genre is defined in a book).

Genres are simply pulled from the genre attribute on a book.  If you delete every instance of that genre, then it will no longer appear.  You can create a smart collection for the genre you want to rid of where the rule is something like 'book genre contains "foo"'  to see where that genre is being defined.  Then when viewing a book in this collection, you just press edit, then genre to set it to something else.