I'm still working my way through all of this to see if I can figure it out. I chose to attempt integration with my Gallery2 install first, instead of trying to bite off a whole custom PHP installation, etc.
The first page has a link to a precompiled version of ffmpeg that will work with Dreamhost. I was able to put it on my server, and configure Gallery to recognize it. I set up "upload from server location" permissions and ftp'd a video to the location. I was able to add the video as an item to one of my albums, at least it said success. When I went there, I got "download this plugin" but hit a roadblock there because the mimetype apparently couldn't be identified.
My plan is to share the proper steps when I get this all figured out, but you should keep doing your own research too. If you're trying to clone a site that is ostensibly worth $1.65 billion in stock, it's going to take more initiative than just asking for detailed instructions.
http://codex.gallery2.org/index.php/Downloads:Dreamhost_ffmpeg_0.4.8
http://ffmpeg.mplayerhq.hu/documentation.html
http://wiki.dreamhost.com/index.php/FFmpeg
http://benconley.net
http://teamshocker.com