How to upgrade the Drupal core.
We've been recommending that you use Subversion to manage your Drupal site, so these instructions are geared towards using it to upgrade.
The instructions also presume that your site can be taken offline during the upgrading process. If you've have a site that you can't take offline while the process is completed, you've got a whole other set of complicated issues to deal with!
These instructions were written based on upgrading Drupal 5.7 to Drupal 5.10.
Prepare the current site