you can update TemplateSwitcher just as any other extension.
First, download the latest version by logging in to on our site, you can find the download link in your account/your orders.
In the backend of your site, go in the menu to Extensions -> Manage ->Install, and upload the ZIP file.
In the case of the TemplateSwitcher, you must unzip the original ZIP file first, as the TemplateSwitcher consists of a module an a Plugin.
Upload/Install the module zip file and the plugin zip file separately.
Finally, make sure that the plugin is activated and the module configured correctly.