Firefox is one of the easy ones to install.
You can either install it as root if you've got more than one person who uses the computer and may want to use FF, just make a new folder in /usr/share called mozilla-firefox and unzip it to that folder. If you want to install it as a user, just make a folder in your file tree called mozilla-firefox again uzip the firefox-1.0.4.installer.tar.gz to it.
In both cases all you've got to do is double click on firefox-installer executable file and it will self install. All of this you should be able to do in the file manager, either root or as a user depending where you want to install it.
Most other programs you download should have a readme file that gives instructions on how to install the program. The lazy way to do that is to uzip the file to a folder and open the readme file in a text editor that cut and paste the commands into either a user console or root console.
There is a Linux version of Macromidia flash player but not Shockwave. I'm not sure about MandrivaLinux because I use Xandros, but I should think yours is similar.