The most secure and reliable way to upgrade is (unfortunately) manual method. I mean, install new Joomla and then copy all things one by one.
If your site is extra large, try jUpgrade tool
extensions.joomla.org/extensions/migrati...omla-migration/11658
but it does not work properly on all servers (don't be surprised if it does not work on yours). Also, this tool does not upgrade component's data. All extensions (modules, components, plugins, templates) must be re-installed manually on the new Joomla.