Honoré Daumier, The Print Collectors,
c. 1860-63. Source: Wikimedia Commons
The principles of researching an artwork are in many ways similar to the principles of researching an artist. Here are some suggested tips:
Compile a list of the different titles an artwork has been known by. Include names in other languages, especially the artist's own language, and especially if you are planning to look for material in those languages. You will generally want to run searches under at least some of these different titles. For instance Vermeer's The Art of Painting is also known as Allegory of Painting.
If an artwork has a very distinctive title, you can search for it by title only. Otherwise, it's best to search by both title and artist's name.
If a work has been attributed to different artists at different times, search under all the artists involved.
Use the price databases if it is possible that the work has been sold at auction in recent decades, and then track down the relevant sales catalogue(s).
If the work is or has been in a public collection, then that collection's catalogues will clearly be a key resource. The collection's library and archive will also be worth a visit. Even if the collection does not advertise itself as holding an archive, it will inevitably have some unpublished material relating to the work, so feel free to enquire. In the case of collections it is not feasible for you to visit, the librarian or archivist may be willing to answer short questions by email.
Some private collections publish catalogues, and in addition may be willing to give you access to any archival material they hold.