I downloaded the Office upgrade as a tar.gz file. How do I install it?
You have likely downloaded the source code for LibreOffice, not binaries distributed by TDF for installation/upgrade from the official download page (they have DEB/RPM/DMG/MSI formats depending on target OS). Another possibility is that some of normal binary format (like DEB) has been renamed to .tar.gz for some reason.
If you need a binary installer, please re-download it from the link above (possibly using a different download program, like torrent). If you want to use the source code to build and install LibreOffice, you would need to get familiar with LibreOffice build process, which is described in our development wiki (not the easiest way btw).
I already downloaded from the official download page. It’s a tar.gz file. I have no idea how to install it.
Did you download the source code? from the section named “SDK and Sourcecode”->“Download the Sourcecode”?