There are several different package formats in the Linux world (see
http://en.wikipedia.org/wiki/Linux_package_formats for some of the more popular formats).
In order to keep things simple and to make it as widely available in the Linux world, the PixInsight folks have used a common, but very very basic form of distribution. The PixInsight package is a compressed tar file, kind of like .zip files used in Windows. The PixInsight application is fairly self contained application and set of files.
I really don't do a lot of gui file management stuff, but here are some command line instructions (with commentary).
Start a command line session
download to a known location (directory) the .tar.gz file that matches the architecture you are running. The .tar.gz file is a compress tar file.
create a new directory (folder) in your home directory, called PixInsight
mkdir ~/PixInsight(the ~ character is a Linux command line shortcut to mean your home directory)
move the downloaded tar file into this directory (lets assume that you downloaded the file to your Desktop folder)
mv ~/Desktop/PI-x11-x86-01.05.02.0503-20090605-c.tar.gz ~/PixInsightgo into that directory and extract the files
cd ~/PixInsight tar xfz PI-x11-x86-01.05.02.0503-20090605-c.tar.gzPixInsight is now installed.
There is a file located in the installed directory that is used to invoke PixInsight
cd(this puts you pack into your home directory)
And if you now enter:
PixInsight/bin/PixInsight.shthis will run PixInsight.
Depending on what desktop (gnome, kde, etc.) you are using, you can create a shortcut or an application icon to launch the program (just invoke the PixInsight.sh file).
If you avoid placing any other data into the PixInsight directory, then upgrading to a new version is very easy.
Just empty out the ~/PixInsight directory and extract the application from the new tar file.
Just a quick comment, I did have a minor problem invoking PixInsight, in that one of the supplied library files has an assumption on the presence of a system library file that was not on my system. There was a very simple work around, but did require me to slightly modify the PixInsight.sh file). But I suspect that Minty (which is based on ubuntu distro) shouldn't have the same problem.
Anyway good luck.