A lot of the sites for hounds, including greyhounds, say that you should use a hound brush on them. Ok... my problem is that I can't find any definition of what a hound brush is, so I have no clue what I should be using! Can anyone describe one of these, or point me to a link? Google didn't help.

I have heard them called a "hound glove". I'm not exactly sure what they are, but I think they have little rubber nubs in the palm that pick up the fine hairs that short-coated breeds shed.
I just looked on petsmart.com, nothing called a hound glove or brush, but found "rubber grooming gloves". I think that may be what you are looking for.