How far does the fair-use doctrine go?
For example, it seems like many popular feature films have become part of the GIF and internet meme culture, where GIFs of various episodes are posted on Twitter and such, seemingly without any permission from the copyright holder. It seems like some sites and/or accounts even revolve their whole business model around these GIFs, is that still covered by fair use, or is someone actually authorises such use and/or pays royalties behind the scenes?
Likewise, I've noticed that many software engineers post various stills of films on their blogs and presentations, some do it with credits, some without.
(All of the above is also quite contrasted with the audio copyright trolling on YouTube, where basically anyone who's ever posted anything on YouTube receives claims for copyright infringement from various agents in the presence of even the shortest audio clips that you'd think should clearly fall within the fair-use doctrine.)
As such, what are the limits, if any? Taking someone's photo and using it on your own site without permission in the above-described cases would clearly be a violation and by no means fair-use; but could I simply take a still of a film, and use it in whichever way I feel like? E.g., if I need a still of X doing Y with a Z background, and see a scene with X doing Y with a Z background in a movie or a video clip, can I just take it? And if so, does it have to be credited, in any specific way?