Most of the time I take snapshots of moments that are likely to be on some site. (I've been doing this for a long time, so I know which shots are good candidates)
Then I do a reverse image search. Sometimes this leads to the right movie, sometimes just to a longer clip which has even more information.
Some studios have a recognisable style which helps narrow things down to the point you can do a keyword search.
It is very rare that I know the answer right away, I have a terrible memory for faces. (I often look at the boobs, birthmarks, scars or ears instead of the actual faces.)
It can take a while, but I find it a fun way to spend some time.