Right, the few times I used tar.gz it was basically just a portable app, which isn't how I think about "installing" programs usually.

Let's use Tor Browser as an example since that's one of the programs that typically gets installed with a tarball. Once you've downloaded and extracted the tarball, you'll want to navigate to the extracted files. You can do this in the terminal using CD commands, but I think it's easier and a little more intuitive to just use your file manager and navigate to the folder that way. Once you're in the correct folder, you'll want to right click on an empty space and select "open and terminal." Now you'll have a terminal open and it will already be in the correct directory. From here you'll want to run the "start-tor-browser.desktop" script. To do this, simply type ./start-tor-browser.desktop and you'll be able to follow along from there.

Running programs from a Tar image typically involves running a script. You just have to change the name of the script to match whatever they have in the directory. Auto complete is your friend here. You don't have to actually type the entire name of the script, you only need to type the first few letters and then hit tab.