The best way I have found to do the manual update is:
1. Make sure you do all of your upgrading on a development server and never on your live site.
2. Backup your app\etc\local.xml & your templates folders in both “app\design\frontend” & “skin\frontend”
3. Login to admin and disable Cache.
4. Open your “var” folder and delete all of the content except for the .htaccess.
5. Download 188.8.131.52 archive and extract the content into your magento root folder. (Replacing all older files and folders)
6. Copy your backed up local.xml & template folders back in to there original positions.
7. Open a browser and navigate to a page on your site, it will take a little longer to load than normal. This is because it is updating your database.
8. Update done. Check your site, you may have to tidy up your template because of the new changes.
NOTE: If you are using extensions or have modified core files you may have problems.
If you have extensions installed and they are causing problems after updating try uninstalling before you update and then reinstall them after you have finished.
If you have made changes to the core files your changes will be removed when updating. (I would not recommend making changes to core files in the firstplace but you can all ways re-add the changes after updateing. *** All ways re-add your mods rather then backing up the originals as you will not get the changes in the new files and will possibly brake other parts of your site.