This works for many 'pseudo-streamed' multimedia files. Youtube is just one of them.
There is really no trick. You just have to know that Internet Explorer already cached the contents on your IE page somewhere ("Temporary Internet Files" folder or "Temp" folder) in your hardisk and try to locate them. As soon as you finished watched the (pseudo-)streamed media, the full file is somewhere on your hard-disk. Use search (for the file type or restrict to size over certain MB and time to the past hour).
For Firefox, there are similar file folders to cache the temporary contents.
To play flash video one can download (and install) a flash-player (only 1.13MB), or use other players of your choice.