How to Update Drupal 8
You should perform a full backup before doing an update. Note that these instructions apply only updating 8.x.x version of Drupal to any later 8.x.x version.
To update your Drupal 8, go to “Reports -> Available updates”…
It will tell you what needs updating. Here we need to download a new version of Drupal.
It will give you a tar.gz file.
2. Put site into maintenance mode. “Configuration > Development > Maintenance mode”.
3. Delete the “core” and “vendor” folders on your webhost.
4. You can extract the tar.gz file and then upload to web server overwriting what’s there.
You can extract it first locally using 7-zip which will give you a tar file and then extract again the tar file to give you a folder (in our case “drupal-8.0.1”) containing the new Drupal version.
5. Re-apply any changes that you might have made previously to any of the files.
6. Sometime a new release will change the “sites/default/settings.php”. You can compare your webhost version of “sites/default/settings.php” with new release “sites/default/default.settings.php” and merge in any changes.
7. Run /update.php on your site.
8. Check “Reports > Status” to see if upgrade was successful.
9. Disable maintenance mode.
The official update instructions here.