Public libraries represent a substantial portion of the book market. As a former professional librarian, I’d like to offer a few tips in tapping into this market. There are always exceptions to the rules, but the following observations generally hold true.
1. Local public libraries are very receptive to including the works of local authors. Furthermore, if your local public library system is a large one with numerous branches, there is the possibility they also will order copies for their branches (if you lived in the Los Angeles Public Library System region and the system ordered a copy for each of their branches, think of the bonanza!).
2. Most public libraries of substantial size (having multiple branches) have on their staff a Collection Development Officer or Acquisition Librarian. These librarians coordinate the purchases and are the people to contact. You can also touch base with the individual branch librarians if need be.
3. Since they don't have time to read every available title, librarians rely heavily on book reviews when adding titles. If you can garner an early review of your book (from a reputable review source), this is a huge help, particularly when it comes to library systems outside your local one. It is best to approach the library market from a geographical perspective---first the local ones, followed by the regional (state). In addition, if your work is set in a particular location, no matter where, look for libraries located in that region. Libraries are always on the lookout for titles to add to their local historical collections (e.g. "Florida Collection").
4. Most public libraries have a "patron request" procedure whereby a library card holder can request the addition of a title. They will usually honor those requests. So, if you have a good friend who is also a library card holder, perhaps they will put a request in for your title.
5. Public libraries generally order through a "jobber" (e.g. Baker and Taylor). Seldom will they order direct from a writer.
6. Public libraries, like the publishing industry everywhere, are heavily into the electronic versions of titles. Again, similar to the print version, request that your book be added to the e-collection.
7. There are state library associations. These groups usually conduct an annual convention where vendors are allowed to purchase booths to display their services or books. Depending on the costs, it might be worthwhile to pursue this option.
8. Most public libraries have Friends groups. They are always looking for speakers, particularly local writers. These groups normally will allow writers to sell author copies at their events.
9. Finally, remember to be polite in your dealings with librarians, they can be of great help in both the research and selling stages of your book.