How are you guys using a nice new hdmi compliant tv, cable box and dvd player with a non-hdmi compliant receiver? What is the appropriate way to hook these up?

There is really no need to run HDMI through your receiver, run the HDMI cable to your cable box or DVD player if they have have an HDMI out. For audio just run optical or coax cables from your cable box and DVD to your receiver.

Yep, unless you have like 5 HDMI components that would need to be combined into one HDMI out to your TV, you really don't need such an animal.

So I'm hooking this up just like I would with component cables and digital coax. Except now I'm just replacing the component cables with hdmi cables?

Exactly

You could always use a switch box like this if you want to spend some more money, but not as much as a new receiver capable of HDMI switching.

But if you go with the HDMI switch, though it's currently back ordered, you can get it at the source for even less dough.