Well, son, I’ll tell you:

Life for me ain’t been no crystal stair.
It’s had tacks in it,
And splinters,
And boards torn up,
And places with no carpet on the floor—
Bare.
But all the time
I’se been a-climbin’ on,
And reachin’ landin’s,
And turnin’ corners,
And sometimes goin’ in the dark
Where there ain’t been no light.
So boy, don’t you turn back.
Don’t you set down on the steps
’Cause you finds it’s kinder hard.
Don’t you fall now—
For I’se still goin’, honey,
I’se still climbin’,
And life for me ain’t been no crystal stair

could you help me identify the extended metaphor in this

Well, what is the father climbing?

i really don't know

What do you climb? A ladder? A wall? What does he say his life has NOT been? What does he tell his son not to sit down on and give up?

Yes, he says life has not been a crystal (perfect) STAIR. He comes to LANDINGS. He speaks of STEPS. The metaphor is a stairway with twists and turns and dark places, etc.

The metaphor is comparing two unlike objects -- his life and a stairway.

23July2022

I knew the poem, but from the first line, I forgot.
…‘Hello Internet.’
Rather than offering a Google; Langston Hughes moment, it immediately hit your page. LOL!

Since this is ‘a hundred moons ago.’
I’m offering some under-standing of the writing/texting ✍️, because I can; the initial conversation was forever ago.

Trying to keep it “cute”, and simple-ish.
The poem offers, from a father to his son, an understanding that is in the life that all is given; that that is like isn’t all ways easy.
Respect that, sometimes, you will have to move forward in difficult situations.
‘But to the father’s son, he tells some possibilities in life, but lets him Know that through it all, his first understanding is simply to live. Be alive!!! ‘It isn’t always easy, but if there is prosperity, LIVE to see it.’ …

no crystal stair

so he's climbing up steps ?