Sorry, I thought you were looking for a new Linux distribution. Do you really want to compile software, or you mean "install"? You probably mean the latter. If you are using the Mandriva distribution, you shouldn't download software from Red Hat's repositories. It may break your system. You should only install the sofware you can see in their sofware installation program. In other distros, like Ubuntu, Debian and PCLinuxOS, this program is called Synaptic; in Mandriva I don't remember, I think it's Urpmi http://soft.zoneo.net/Linux/install-software.php
On the other hand, if you really want to compile sofware, you should download the .tar.gz archives in sourceforge http://sourceforge.net/
. Then you have to unpack the compressed file, and then use the command line. Usually it involves typing "cd ./Desktop/programName" (assuming you unpacked the tar.gz file in that directory) and then typing "./configure" then "make" then "make install". But that's not always the case, so before doing that, you should open the directory where you unpacked the file, and search for a file called README, which will have the exact instructions of how to compile. Sometimes it just works, but sometimes you have problems with missing dependencies and the like, so it's definetely not the easy way to install sofware. Another way to install software is to get a ".rpm" package in some website that says it's compatible with your distro (which is currently Mandriva, right?) and then install the package using the KPackage program, or another similar program.
On the other hand, you can try another distribution like PCLinuxOS, Debian or Ubuntu, but you don't install it on top of Mandriva, you install it instead of Mandriva. You can have more than one distribution in the same computer, but you can only run one of them each time you boot your computer. When you boot your computer you get to choose which distro to use, or even to use Windows. It's called "dual booting" or "multi-booting". There are programs like VirtualBox or VMware that allow you to run a simulation of other distros or a simulation of windows inside your distro. It's called "virtualization", but that's another story and it's not quite the same as running them "native".