The thing here is not the legislation of making an AMV (which as KM said, you can do as long as you do not profit from it without consent) but actually getting a digital copy of the film. If you own the DVD you can rip the file from it legally for your own use (providing whichever software you use to do so has been aquired legaly). I think you also can share the file with others IF they have the Film also but, lack the software to rip it from their DVD. If either parties do not own the film, they have not payed for the file they are using, and as we all know, the act of taking something you have not payed for falls under theft.
However, some media will forbid you from doing this, and if you then go ahead and upload / download them, you have broken the law. Even if a site claims that you can download "Film title here" "100% FREE AND LEGIT NO RUBBISH" doesn't mean it is. If I told you that I know the next winning lottery numbers for your area, would it be true?
These file sharing sites are almost all illegal, even when you pay for them, wether they use P2P or their own servers even. The only thing that changes is your bank balance, and the random guy you just gave that money to. Further, the only reason these sites are still up and running is because in small print on their terms of use and conditions (which most people do not read) they state that they are not to be held responsible for whatever you use their site for (illegal downloads). So not only are you then breaking the law, you pay for the privilige to do so.
I'm not saying anyone here is breaking the law or anything, i'm just saying to OP be careful of where you download things from. Most ISPS will not take much notice to the odd download, but start doing it too frequently and you will be cut off from your ISP aswell as recieveing a hefty fine if the company chooses so (and they will) Click here for a true story.obviously in that case, it was music but the same applis to films, just that the fine is often worse.