Hi Phil…No worries, the first time doing this can be scary for some, but overall it’s fairly easy to do. First backup your current theme just in case anything goes wrong, you can revert back. Next you would download the theme from the original email download link (hopefully you kept that), unzip it (the preference.zip file) to your desktop, then use your FTP to upload and replace the existing theme files with the new ones. Please note that this will overwrite all files, so if you made changes to any core files, make note of them. Once done you should be updated.
If you have a theme membership here at Styled Themes, then you log in and click on “Download Themes” on the top main menu, then unzip the theme preference.zip
The reason why you do not get notification in your Dashboard is because this theme is not provided through the WordPress.org website which is why only the free themes from their site show up in the search and show when updates are available. Themes from third party sites other than wordpress.org will not have that ability (hopefully they will one day).
You mentioned you are using a child theme which is good, so technically overwriting the theme files of the parent theme (not the child theme) will not lose your modifications then. But I still recommend backing up both the parent and the child theme if you can before doing this update.
It’s always a good idea to read the theme (any theme) Changelog.txt file first.