It will be in 480p quality I believe, rather than 720p or 1080i it came in....
If you have deep pockets, you could buy a Blu-Ray recorder. Then you could keep the Hi-Def.
And more than likely, the Direct TV box is hooked into the TV via HDMI (looks like a computer connector) or Component (Blue, Green, Orangish red, Red, White).
More than likely, you will need to get some RCA cables (Red, White, Yellow) to hook it into the INPUT of the DVD recorder.
A DVD recorder should be around $100.
Just holler if you want/need more help!
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Live your life in the Kelvin scale..........Stay Positive.