Drupal 7 has a built-in updater that updates everything that needs to be updated. However, it requires FTP access but we use SFTP so it does not work. Luckily, we can use drush instead.
Read through the update changes for every module before you update. Some updates requires you to do some changes
Use ssh to access the server:
Change directory to the public folder:
drush -y up
Let drush run and you should have an updated website.