Prior proceeding with the application upgrade it is recommended to create a full web site backup. Detailed instructions can be found in the backup section of the SiteGround cPanel tutorial.
If the web site is installed through Softaculous, you can use the built-in upgrade functionality:
http://hostlantern.com/clients/knowledgebase.php
Alternatively, you can upgrade it from the Joomla admin area. Log in it and navigate to Extensions -> Extension Manager. Open the Update section. Click on the Purge Cache button and then on Find Updates. Once an update is found, select it and click on the Update button.The script will be automatically updated to the chosen release.
More details about the upgrade procedure are available in our Joomla tutorial:
http://hostlantern.com/clients/knowledgebase.php
Joomla is a powerful software that is easy to work with once you have the right host to support you. Before you lose any more time with the wrong host, check out the hostlantern Joomla hosting offer.