You can choose any plugin you are familiar with other than discussed below.
Always better to keep backup : Update : Important Considerations

Install and activate Plugin

• Go To : Plugins > Add New
• Search for : Easy Theme and Plugin Upgrades

  For more help related to plugin : Plugin direct link

  
• Install and activate plugin.
• Get latest zip file of theme
• Go to Appearance > Themes.
• Click the “Add New” button at the top of the page.
• Click the “Upload Theme” button at the top of the page.
• Browse for the theme zip file with the new theme version to install.
• Click the “Install Now” button.
• Activate theme after updating finished.