Ive only done this on PS3.
So you have rendered your clip in theater mode in the vault and get a message telling you something like, If you want to view these clips visit theater.callofduty.com. Well I cant get on theater.callofduty.com I just get an apologie message about how they have issues FAIL!!!
and unlike BO it dont upload your clips to your own youtube channel either.
BUT if you visit YouTube and search your PSN name you will magically find the clip you rendered on a channel called PS3codMW3 WIN!!