Usually, when I've conducted "research" to learn more about what's expected and conventional in a particular category (whether or not I intend to subvert it, which I often do), it usually takes the form of simply browsing the actual stories on Lush in that genre so I can get a feel for it. However, I have recently done deeper research on two stories, which involved hitting the search engines and diving down some rabbit holes.
For "Heartbombing the Heartland," I did quite a bit of research, much of it on Google Maps, on specific locations across the Great Plains. Especially Valentine, NE, a place I've been through once, but didn't know too much about, but quickly learned was the perfect setting for the ending of my story. I also took great care in choosing the names and pseudonyms of my artists, searching again and again until I came up with ones that didn't correspond to actual prominent artists.
"Steam Mates" took more research than I've ever done on a story. That included what was going on in 1972, in Portland, OR, in current events and in popular culture. That included whether specific businesses were in operation in Portland that year, what the state of the Watergate hearings (and other major news events) was in August of that year, and what the most popular and/or well-regarded movies, TV shows, books, songs and albums were that year. I verified release dates to make sure I referenced only what would actually have been available in early August, and not stuff that came out later in the year. I went out on a limb with Mott the Hoople's "All the Young Dudes," which had not yet been released in the US, but had been out in the UK for a few weeks, assuming that Portland's Music Millennium would have procured a few import copies around the time my story is set. I also did quite a bit of research on 1910s-1920s steam cars to understand how they worked, and to project how they might have evolved over the next fifty years if internal combustion hadn't killed them off.
Both my upcoming Supernatural story for Christmas, and my Fantasy/Sci-Fi story that will put me across the Omnium finish line early next year, will each require a fair amount of research in terms of reading multiple books and watching several movies that relate to the subject matter.