I've just passed a kidney stone and the pathology came back as it
being both a calcium oxylate stone and a uric acid stone.  My
urologist said he'd never heard of that and had them re-test with the
same results.  What kind of diet do I follow now to try to prevent
further stone?

Fluid intake is generally accepted as the most important factor, but
don't go crazy as there can be adverse consequences from excessive
fluid intake.
There are some useful general guidelines here:
http://www.nym.org/healthinfo/docs/081/doc81dietary.html

I have had repeated kidney stones as well as gout, so I also must
avoid calcium oxalate and uric acid (purines). If you do research on
this, you will see how overwhelming and contradictory the advice can
be from various sources.  What has worked for me is increase drinking
water, cut down on raw meat and moderately cut down on other protein
(uric acid) and cut down on dark vegetables (calcium oxalate).  Also,
you should eliminate liver, gravies, and alcohol consumption.

I wrote "raw meat" above, but I meant RED meat.

Thank you all for your comments and suggesions; I will heed all!!!