The idea that I might be able to get my book on store shelves is almost too much to wrap my head around!
Only a commercial publisher has the distribution and resources to get your book shelved in any store.
If that is your goal then get to a store, check their poetry section, and note down the names of the publishers of those poetry books. Then begin the submission process, following their guidelines.
Poets used to be the rock stars of literature, not so today. It's hard to sell and to a small market. Many poets turn to self-publishing, which is perfectly fine, but they know from the start their books won't be in stores.
Kindle Digital has been suggested, paired with Amazon Digital Services for print on demand copies.
https://www.amazon.com/gp/seller-ac...d=AZFooterSelfPublish&topic=200260520&ie=UTF8
Here's the catch: You HAVE TO READ everything in their rules until you thoroughly understand what everything means. If you don't, bring questions here to AW for help. You've got about 7,000 friends to watch your back, so don't be shy about asking. What you don't understand can be a problem down the road.
Your Kindle version and the Amazon digital version will get their own page on Amazon.
You can order your own copies of the book to hand sell at events. For everything else, you set up a nice website, a Facebook page, do the Twitter thing. Again, don't expect clamoring fans anxious to read your words, poets don't get no respect, and there's lots of competition. You're doing this out of love, not to make money.
That said, here is a legit organization to check out:
https://poets.org/
Above all, NEVER pay to publish. The vanities and other rip offs will promise the moon and praise your work to the skies, but all they want is your money, period. They cannot get your book into stores, not ever. Stores and libraries are on to the scams and do not shelve such books. Stores don't have room for all the commercially pubbed titles released each year, never mind the vanities and indie writers.
Next: go to the library and see if they have a copy of Poet's Market. Read it. If they don't, they can borrow from another library for you.
https://www.amazon.com/Poets-Market-2019-Trusted-Publishing/dp/1440354391/
It will have information you need to navigate publishing this specialized literature.
Please be aware that scammers are well aware that poets are desperate to get their words out and they will have tons of ploys to grab their money -- all the time being VERY nice about it! So the more you know about the business side, the safer you will be from the sharks.
https://poets.media/poetry-publishing-scams-to-avoid
http://www.writing.org/html/a_poetry_scams.htm
One of my friends got taken in by these rotters. He was told his poem would be the featured work in a prestigious collection. He did have to help with "production costs" and buy a certain number of copies. He lost a bundle on that one and sadly, still thinks he won their "contest." The reality was a softcover book where his poem was mushed in with 800 *other* poems. It cost a LOT.
Many of these scams prey on schools, which makes my blood boil. The kiddies make up poems, the "service" puts out a winners collection, and 500 parents are out 80 bucks each (often more) to buy a copy that cost 3 bucks to print.
So keep writing, but be careful out there!