I don't have any problems installing .deb files, but when it comes to tar.gz, then nothing happens. I extract the files but that is it. How do I get throught this installation



When you say install, what do you mean? When it comes to website software, there isn't anything you need to install to your computer. All you have to do is extract the files(which it appears you have already been able to do), and you upload those files to some online database via an FTP client such as FileZilla or SmartFTP(I'm not sure if SmartFTP is on Debian distros, but as an Ubuntu user, I know FileZilla is).
I hope I was able to help.

- mbc

Well, once I've extracted I must be able to open an application?

Which application(or type of application) are you attempting to open? The only application you need to open when it comes to uploading files for a website is an FTP client, such as the two I previously mentioned.
Also, to install Drupal, open the files and select all of them. Drag those files into a folder on your website via an FTP client, and that will do the rest of the work for you.

- mbc

The required binary applications are the webserver (presumably apache) and the database server (presumably mysql), both of which are standard parts of any Linux distribution.

You do not need to install Drupal as a .deb file -- just untar the .tgz directory structure and place it in your webserver's document directory. For use on your computer, that is simply a matter of dragging and dropping the file tree where it belongs. For a remote server, you can use an FTP client such as gftp, or do what I do -- mount the remote server as a directory using Nautilus. Now your remote filesystem acts as if it were local to you.

The only safe way to use .deb file to install Drupal would be to use the Acquia distribution, which leverages the Mint/Ubuntu/Debian environment effectively and -- this is important -- properly updates you for security and bugfixes.

So by an application, Fernand meant a web server such as Apache?
Sorry if I caused you any confusion if that's the answer that you were going for.

- mbc