Ukiyo-e prints were marketed as relatively affordable home furnishings to the increasingly prosperous urban middle class of the later Shogunate and subsequent Meiji years.

They were mostly marketed and sold by publishing houses big and small, though of course some artists did private work and some studios would have made small, non-commercial runs of certain prints.

Finding the publisher's mark is straightforward, it should be one or more characters in a box or circle near one of the corners of the print. Matching that mark to any meaningful information is a much tougher task. In both English and Japanese collecting worlds, the role of the publishing house in ukiyo-e has long been ignored in favor of the artist.

The authoritative book on the subject is Andreas Marks' Publishers of Japanese Woodblock Prints: A Compendium with over 2,300 different publishing marks, and collectors of rare prints are still finding new marks to this day.

Edit: Mark's book is out of print and even a used copy is worth several hundred dollars. I would recommend making an inter-library loan request if you have access.