Updating Drupal 8 using Composer and Drush

First check if your site needs updating:

composer outdated

On the development site, run the following commands to update Drupal:

composer update
drush -y updb
drush -y entup
drush cr

Upload composer.json and composer.lock to the production site, backup up your database, then run the following commands:

drush sset system.maintenance_mode 1 && drush cr
composer install --no-dev
drush -y updb
drush -y entup
drush cr
drush sset system.maintenance_mode 0 && drush cr