How do I connect my Direct TV Satellite Box to my Sony VCR/DVD Recorder And my Sharp TV?

It depends on the box.

If it's an HD DirecTV box and a Sharp HDTV, then it would be HDMI out of the DirecTV to the TV, composite video out from the box (yellow, white, red) into the recorder. Out from the recorder for VHS would be another composite connection in to the TV.

And then, depending on the unit, for better DVD picture quality it would be HDMI or Component (red, green, blue for video instead of the yellow for video) to the TV