How to update Drupal core
Here is how to update Drupal in order to keep it at the latest version for better security. This assumes that you are doing an update for Drupal 7 version with another Drupal 7 version (for example 7.30 to 7.31) — not going from Drupal 7 to Drupal 8 (that is an upgrade).
1. Make full backup for site files and database (you can use Drupal Backup and Migrate module)
2. Download the latest version from drupal.org
3. Put site in maintenance mode by “Configuration -> Maintenance”
4. Delete all site file except the “sites” folder.
5. If there are any other files that you have modified (such as .htaccess or robots.txt), merge those changes into the new version.
5. Extract and upload the new version files from your download (except for the “sites” folder).
6. Check if there is any changes to the new version’s /sites/default/default.settings.php file. If yes, upload and replace. And merge in the same changes into the settings.php that is on the server.
7. Run /update.php as admin
8. Turn off maintenance mode.