I made slow progress today, mostly because of my unfamiliarity with the tools greengeeks (my web host) gave me.
First, I update my live site to bring drupal to 6.20 and zen to 6.x-1.2 which were the only items needing update. Since drupal really wants you to backup before doing a core update, I thought I would simply copy the tree starting with document root to a new subdirectory. This mostly worked except for the few items in protected subdirectories, e.g., config.php. Once I figured that out, it was a simple matter of changing permissions and copying, but only after wasting a bunch of time.
Then I copied the updated live site to test.ollieweb.org (watching for the permissions issue this time). After a little mudlling around, I updated the config.php file to point to the new document root.
Then I realized I needed to create a new database. This link summarized the process pretty well, but I eventually found that I needed to use the mysql tool in greengeeks’ control panel to create the new database and to set up the new user for it.
Once that was done, I had a new site on line.