Poetry Books are in the 800s in the end numbered shelves of the library. You will find that you are welcome at many college or high school libraries. Some may not be willing to issue you a card unless you are a currently enrolled student but will allow you to read in the library. Another resource for free books is Internet sites where you can view or download whole books. It may take a little extra time to download or print out the available books.
Some cities have book exchanges at used bookstores.
In a book exchange you can bring in any kind of books and exchange them for credit on books you want to buy in the store. Often they will trade you one book for two you bring in. You can pass on books you no longer need and get books you want. So here are some sources of poetry books. Get in the habit of looking at several of these resources.