Updating from core 8.7.9 to 8.8.0
In your composer.json file (found in the root of your drupal site) find the line "drupal/core": "x.xx" and change it to "drupal/core": "~8.8" and then run composer update drupal/core --with-dependencies

Also, don't forget to run your database updates after! (run drush updb or go to your-drupal-site.com/update.php)