Copyright and fair use: how does it work?

Hi all!
I would like to publish educational videos about several topics, from animal evolution to historical events, but I'm confused about what kind of contents I can use without having troubles with copyright.
I see many people using pictures/videos, also without giving credit.
In some cases, they may use screen captures (for example, I want to talk about gorillas, I show you the wikipedia page about them) or cell phone videos (for example, I want to show you a scene from a movie, I film the movie on my tv).
Given that some of them are obviously infringing copyright, is it okay to use such contents if your video is educational (and you give credit)?

Thanks