Download and enable Admin Menu
Download and enable Backup & Migrate
Backup /htdocs/sites
Backup database with Backup & Migrate module
Put site into offline mode
Change theme to Garland
Disable contrib modules
remove Drupal files from /htdocs
Download and extract new Drupal files to /htdocs
Copy orginal /htdocs/sites directory into new Drupal files.
Change system user permissions for contrib modules directory.
Run http://drupaladmin.net/update.php
Change to normal theme
Run http://drupaladmin.net/update.php
Enable contrib modules.
Run http://drupaladmin.net/update.php
Verify content is there, featuers are working, and your status report.
Backup everything once it is up to date.
