You have at least 3 options that I can think of:
System->Administration->Synaptic Package Manager
And a 4th one, download the source of whatever you're installing, make it and install it.
Actually now that I look further at your query, you have to do #4 I believe because you have a tar.gz file.
tar -xvf <filename.tar.gz> will extract it.
Look for INSTALL or README and check on how to build and install it.
Likely you would have to:
- change to the directory where the sources got extracted, and likely that directory was created by the extraction.
- In there, type "./configure"
- After that is done (providing it succeeds), type "make"
- After that is done, type "sudo make install" and put in your password, or you may have to become root if your user is not allowed even sudo privileges.
But check with the extracted documents to make sure that the typical "configure/make/make install" flow is how to build and install their application.