What encoding settings does Revision3 use to get quality high but file size so low? I am creating my own content. We have recorded uncompressed, and are now at the exporting stage.

This video will be downloaded, not streamed via YouTube or Vimeo. So far, we are rendering it at 5Mbps bitrate and it is coming in at very high.

It ranges from 23MB/minute to 38MB/minute for 720p high-def quality (mp4).

However, I know that many videos downloaded from the internet, for example - 

Film Riot - has an HD file that is 84.5MB for 10:11 (so that works out to about 8.45MB/minute). The quality still looks nice...not necessarily THE BEST....but definitely pretty decent.

Film State - has an HD MP4 file that is 203.5MB that runs 25:50 (so that works out to about 7.8MB/minute).

HD Nation - has an HD MP4 file that is 236.2MB that runs 17:55 (so that works out to about 7.8MB/minute).

How do I get it so low, but quality still being so high?
Your best bet for high quality and low size is 2 pass variable bit rate, but it is worth noting that the size of the video also has a ton to do with how much motion it contains and how often the scene changes.  One of the most popular modern codecs to use for such compression is h.264.

Video compression works by looking for similarities not only within one frame, but also between nearby frames.  They more similarities there are, the less data it takes to represent it at a given quality.  Variable bit rate seeks to maximize quality by using the most data where it is needed and saves data where it is not.  Using two-pass allows the first pass to figure out what the best places to use the available data are before actually making the final compression.