Well, it looks like your receiver on the Yamaha system has 4 HDMI inputs, pick one, and plug your Magnavox into it.
To record cable, plug composite (yellow/red/white) from the cable box into the Magnavox inputs. There is a row of white, red, then yellow inputs on the back labeled IN which you should use.
This will allow you to record composite video cable television content in standard definition on your DVDR/VCR unit.