Check for available updates: drush ups

Put site into maintenance mode before updating using:

drush sset system.maintenance_mode 1
drush cr

Then execute the updates:

Update Drupal core: drush up drupal
Update a single module: drush up module_name
Only apply security updates: drush up –security-only

This is a more selective/cautious approach to updating everything with drush up

Next, apply any required database and entity updates:
drush updb
drush entup

Now check your site is OK – look at the status report page, test the site, and finally turn maintenance mode off if applicable:

drush sset system.maintenance_mode 0
drush cr

Finished. Go to admin/reports/status to check for errors.