Download the latest release of your current Drupal version.
Extract the [tar ball or zip] Drupal package.
Set your site on maintenance mode.
Delete all the files & folders inside your original Drupal instance except for /sites and its sub-folders. This assumes that all of your custom work - including themes - is in the recommended spot - the /sites folder tree. If you have made custom changes elsewhere you will need to either preserve them or plan to replace them later.
Copy all the folders and files except /sites from inside the extracted Drupal package [tar ball or zip package] into your original Drupal instance location.
Some updates do not include changes to setting.php and some do. If the update release includes changes to settings.php you will need to replace your old settings.php in …/sites/default/ with the new one, and then edit the site-specific entries (eg database name, user, and password) in the setting file.
If you have modified files such as .htaccess, web.config, or robots.txt re-apply those changes to the new files.
If you have a favicon.ico file that was deleted replace it too
Login to your site as administrator or as user no 1