English Help: I think I need help describing possessive nouns?

The apostrophe is there to indicate possession. It is required.

Pleiades’ son = the son of Pleiades.

Black swan’s song = the song of the black swan.

Black swan’s songs = the songs of the black swan (his whole repertoire)

Black swans’ songs = the songs of several or many black swans.

Jacob’s ladder = the ladder of Jacob.

Hell’s Angel = one of them
Hell’s Angel = two or more

edit: Sorry. I meant “Hell’s Angels” to indicate two or more of them.

Hell’s Angel’s song = the song of one member of the group
Hell’s Angels’ songs = songs of the group of bikers, if there are such
Hell’s Angels’ song’s tune = the tune of one song of… you know
Hell’s Angles’ songs’ tunes = the tunes of the songs of the… and so on

Your description is correct: “Black Swan’s Song”.

it is correct. had the swans been plural possessive, you would say ‘The swans’ Song’

Simple rule so you won’t need to ask next time:

You always need an apostrophe and you always need exactly one ‘s’*.

If there is already an ‘s’, so as not to split up the word, simply add the apostrophe behind the last letter.

Swan sings
-> Swan ‘s song

Swans sing
-> Swan s’ song

* “Its” is a common exception. This is because “it’s” already has a different definition (“it is”). Very poorly planned ;)