You'll need to get a device that can record from the video and audio put out by the DVR. There are several options, but you'll have to really look for what you can use prior to selecting.
For example:
What kind of outputs does your HD-DVR have? Does it have only HDMI? Does it have component? Does it have s-video? Does it have just composite? Does it have left/right audio out only, or does it have optical out for audio?
Next is the software you will use - some of this will depend on the extent of the feature set you want, and how much you're willing to spend, and what hardware you want to use for the capture process.
For example, I know of off hand, 2 configurations that would work for me.
I have a Hauppauge HDPVR capture device and for TV service, I have an HD DVR from Direct TV. My HD DVR has component out, composite, HDMI, analog 2 channel audio, optical audio. I can hook up my Hauppauge to my HD DVR via component for HD video and optical audio for high quality digital audio that supports 5.1 sound.
To record off of the HD DVR through my Hauppauge, I have (that I'm aware of) 2 major choices in software for the mac:
HDPVR Capture from:
steventoth.net » HDPVR Capture
and
EyeTV from:
Elgato products
For me HDPVR capture is my best bet because it's inexpensive and really easy to use, and doesn't have extra features I just don't need. Once the video is captured, I can convert it, edit it, rescale it for SD to use on a DVD, etc.
I capture in HD because most of the time I don't put it on a DVD and I want high quality that I can play back on my home theater Mac.
Your choices may be different. For you, I'd probably look at EyeTV first since you don't appear to have any capture hardware and they have a large compatibility line listed here:
EyeTV 3 | Technical Information of different capture devices. Elgato also sells some capture devices as well.
My choice was convenient since the Hauppauge was a carry over from when I switched from PC to Mac.
Hope this helps!