If you want to research the publication history of a given text (who published it? how many editions did it go through? what did it cost? how well did it sell? are there any records of the publishers' decisions about it?), you'll probably find that this is a trickier question than it initially looks. Records for sales figures and prices can be hard to find, especially for books published before the 20th century. Some of this information is in publishers' archives, and some of it doesn't survive. But take heart! There are often ways to work around this kind of question.
Bibliographies, both in print and online, can supply you with basic information about when and where different editions of a text were published. See the English Short Title Catalog and the C19 Index (listed on this page under "Online Bibliographies" and "Databases for Historical Publication Research") for comprehensive bibliographies of books published in the British Isles and North America through the end of the nineteenth century. The Early American Imprints series (now a database with page images and searchable text) began as a bibliography of early American publications, and you can still use it to explore editions, publishers, and dates of publication. You can also search BobCat for "bibliography" and your author's name, using the "Subject" search option, to see our holdings for bibliographies of works by and about that author.
Biographies and critical studies of authors can also provide information about the publication histories of individual works, and are worth checking. If your author's letters or diaries have been published, you can try looking for references to correspondence with their publishers. You may also want to search in BobCat, WorldCat, and/or a general database to see if anyone has already published anything about the publisher(s) you're interested in.
More suggestions for this kind of research can be found in Literary Research and the British Romantic Era: Strategies and Sources by Peggy Keeran and Jennifer Bowers (Scarecrow Press, 2005), chapter 11. It's specific to Romantic-era research, but applicable to other periods as well.
Finally, if you want to pursue archival research on a publisher, you can look for where your publisher's records are held using a database like Archive Finder or ArchiveGrid -- with the caveat that you may not find anything.
These databases allow you to search for recent information about publishers, the publishing industry, and books currently in print.
Use these bibliographic databases to find publication information for books in English from the beginnings of printing to the end of the 19th century.
These databases include records for secondary as well as primary sources.
The Society for the History of Authorship, Reading and Publishing was founded to create a global network for book historians working in a broad range of scholarly disciplines. Research addresses the composition, mediation, reception, survival, and transformation of written communication in material forms including marks on stone, script on parchment, printed books and periodicals, and new media. Perspectives range from the individual reader to the transnational communications network. With more than 1000 members in over twenty countries, SHARP works in concert with affiliated academic organizations around the world to support the study of book history and print culture.