For the most complete documentation for upgrading an existing Drupal site, see
http://drupal.org/upgrade.
Instructions on how to update Drupal core with a newer version of Drupal of the same category or same base version [ ie Drupal 6/7/8]
1. Make a backup of your Drupal instance.
2. Download the latest release of your current Drupal version.
3. Extract the [tar ball or zip] Drupal package.
4. Set your site on maintenance mode
5. Delete all the files & folders inside your original Drupal instance except for sites folder
6. Copy all the folders and files from inside the extracted Drupal package [tar ball or zip package] except sites
7. Paste into your original Drupal instance
8. Login into your site as administrator or user no 1
9. Go to yourdrupalsitename/update.php
10. Follow the process to update your Drupal instance
11. Disable maintenance mode