Updating drupal modules
Running from within your Drupal 8.3 and lower site will generate a SQL file with your database backup and a tarball containing your entire codebase along with the files directories.
After creating a backup of your site, the standard update procedure involves putting your site into maintenance mode.
Functional Drupal sites are composed of three components: code, files and a database.
Hopefully the codebase for your site is already stored in some type of version control system.
With your site in maintenance mode you're now ready to update the codebase to the new release.
The following steps should be run on a local development or staging site and then deployed to the live site using your regular deployment process.
As such, the impact of a patch release is genuinely quite minimal, but may be important to address in a timely fashion, especially in the case of a security release.
On our blog we walked through a simple Drupal 7 to Drupal 8 migration which might give you a sense of what could be involved in the process.
Once you've determined whether your update is a minor or patch update, it's a good idea to read the release notes.
These will provide a high-level overview of the changes that have gone into the new version.
While I would recommend being familiar with all of the methods, they accomplish the same thing.
Regardless of which method you wind up using to update your Drupal site it is always a good idea to make sure you have a fresh backup available.