How to Update Drupal Core Tutorial
Step 1 : Make a complete backup of your Drupal (including files and db).
Step 2 : Download the latest release of your present Drupal version you want to update from this URI. https://drupal.org/project/drupal Extract the archive(.zip or .tar.gz).
Step 3 : Place your Site in maintenance mode ( Configuration » Development » Maintenance mode » "Put site into maintenance mode" select the checkbox and hit Save button.)
Step 4 : Remove all the files & folders inside your present Drupal directory except for /sites directory and if you have added any custom files or directory elsewhere.
Step 5 : Place all new files and directories(from Extracted the archive from Step2 and Step3) except /sites directory in your present Drupal directory.
Step 6 : Optional Step If new(extracted archive) settings.php (sites/default/settings.php) different from your current settings.php(sites/default/settings.php) replace it and copy database details (name, user, password,etc).
Step 7 : Optional Step If you modified files in .htaccess or anything else make sure you replicate them.
Step 8 : Login as administrator in your Site now.
Step 9 : Open settings.php in text Editor (sites/default/settings.php) Change $update_free_access = FALSE ; to $update_free_access = TRUE ; Run update.php by for example if your Site is in local mac navigating to http://localhost/Your_Site/update.php
Step 10 : Follow the Steps there to update your Drupal.
Step 11 : Place your site back to live by removing it from maintenance mode ( Configuration » Development » Maintenance mode » "Put site into maintenance mode" Un-check the checkbox and hit Save button.) and Open settings.php in text Editor (sites/default/settings.php) Change $update_free_access = TRUE ; to $update_free_access = FALSE ;