Before you update drupal be sure you have a working backup.
# Backup all the files through ftp with FileZilla
# Backup the database (i.e. with phpmyadmin)
1. Put your drupal website into maintenance mode
Administration > Configuration > Development > Maintenance mode
2. Download the latest drupal: https://drupal.org/project/drupal
3. Remove all old core files and directories, except for the ‘sites’ and ‘themes’ directory
and any custom files you added elsewhere.
In my case this were the folder includes, misc, modules, proflies and scripts and all the files in the root folder.
Don’t delete your temp foler.
4. If you made modifications to files like .htaccess or robots.txt, you will
need to re-apply them from your backup, after the new files are in place.
7. Apply pending updates
8. Check if your site still works
9. Disable update.php by changing $update_free_access to FALSE in sites/default/settings.php
10. Disable maintenance mode.