Sometimes you will get a copyright claim email from youtube explaining that the original owner has filed a copyright claim, but it explains that there is nothing you need to do, are not in trouble, and can keep your video up (it actually says exactly that). What will happen is that they will place ads on your video but give all of the proceeds of those ads to the original video owner. The original video owner will also have access to statistics from your video. So if you go this route you obviously cannot monetize the video and or collect any revenue from it.
There are millions of 'fan made' movie trailers, music videos, etc. on youtube all using movie clips, etc. But those folks aren't getting the proceeds from their videos. Universal Studios, or whoever owns the footage is.
On more original performance pieces we have used in the past we have actually reached out to video creators to seek permission for use of some or all of their original work. For example our video FORGIVEN is a performance piece done by someone else, but we reached out to the video director (Duncan) and the dancer in the video (Dorotea..who is fantastic. You should check out her other videos) and they were kind enough to let me chop up their original video and edit it to specifically fit our song.
But when I throw together a quick teaser or quick video using clips from the trailer to the movie THE MUMMY, I'm not reaching out to Tom Cruise or Universal Studios to ask them. They just file the claim and take any money generated from my video.