If you have Google Apps for Business, Google Video is still the preferred method of storing videos "in the cloud": it is easier to embed into Google Docs and probably more importantly – it can be truly private (you can only access it if you are logged in with the correct account – as opposed to YouTube where you can "hide" the video, but still anyone with the link can access it).
To post a high quality video to Google Video you only have to do:
- Upload the video
I kid you not :-). While initially the uploaded video is of poor quality, apparently it gets processed in the background and later on (in my experience: it takes around 30 minutes to process 1 hour of uploaded video) a high quality version will be available.