tars are archives so the more appropriate term is to “extract” them instead of install. xz is a compression applied to the archive so it is also common to hear “decompress” too.
You can extract the compressed archive with the tar xvf <archive name> command. If you’re not sure how to use a command you can read the manual with the man command (e.g. man tar).
Unfortunately, I can tell you Teamviewer is going to be problematic because it has a dependency on an older library that Clear Linux is not packaging due to known vulnerabilities. See Own to install Teamviewer in Clear Linux?
I don’t think xz is installed on clear Linux by default.
So before you use tar you would have to install xz with:
`sudo swupd bundle-add xz’
Then you can do: tar xvf <name of archive file>
If you don’t need team viewer specifically consider using the Chrome Web browser for remote desktop.
If you install Chrome (how to install below) and go to chrome.google.com/webstore and search for “Chrome Remote Desktop”. You can use it with Android/iOS apps and also install it from the computer you want to use to access the other computer. It doesn’t have file transferring capabilities so you would have to use Google drive or dropbox.
See this link for installing Chrome:
Chrome Remote desktop is free but if you would like to use only open source you would have to look at vnc-server. However you will have to configure firewall rules on your internet router if you want to access vnc via the internet. Chrome remote desktop just works without any changes to your router firewall.