My method:
- Full database backup
- Backed up via FTP all of the plugins, theme files, contents of wp-content/uploads
- made a backup list of all of the custom code I'm using in PHP widgets, as well as the Widget Logic code for each widget
- deactivated all plugins
- ran the auto-update
At this point, I was told the update was done and had gone well. My site looked awful, of course. Content that should show only on certain pages or in certain categories was all crowding onto the front page.
I went back into the plugins admin area and re-activated them one by one, checking the front page and admin area each time. When I got to the Custom Post Templates plugin and activated it, I got parse errors. The Front Page Manager made everything go kaflooey.
I had read in the WP forums that some people were having problems with post scheduling. Since we use that feature a lot, I tested it right away. I set a test post to publish 10 minutes in the future. It worked. I hope it works for days or weeks in the future. We'll see.
So far, so good. I wish all of you luck with your upgrades!