The Publishing Industry is full of weird cycles of events.
As difficult as it is to write a book, it is equally easy to publish it. And as easy as it is to publish a book, it is equally difficult to advertise it.
Each year, I publish two books (2023 is an exception year though). Design its cover page. Typeset it. Proofread it. Edit it. And publish it. All by myself.
And it costs me ZERO charge to do it all.
Yes, publishing is always free. The charges publishers take are for additional services they provide.
If you want to get deep insight into available publishers and their types, read this answer of mine:
Poetry is a very risky genre for Traditional Publishers. To avoid financial loss, they only publish poetry collections by famous, rich or highly-followed on Instagram personalities.
However, for self-publishers, all you need to do is pay their asked sum. And you are done with the publication of your book. No matter what the content of your book, genre, plagiarism, etc.
If I have to advise you personally, don't directly jump at publishing your poetry book. Post your poems on Instagram, Quora, etc., and build a network of your readers.
Once you are satisfied that your book can do good selling only with organic marketing, it’s the time to turn your poems into a paperback.
Yet, in simple language if I have to tell you how to publish a poetry book, then -
Contact a book publisher like NotionPress, BlueRose, OrangeBooks, etc. If you want to go for traditional publishing, pitch to publishers like HarperCollins, Penguin, Rupa, etc.
Convey your concept and idea of the book to the publisher.
Let them handle the rest.
Good luck for your future endeavors.
If you have any specific questions, ask in the comments or you can directly text me.
~ Pravin Gupta