Welcome to the wonderful world of Linux (and it's package management)!
There's two ways you can go about installing software (or packages as is more common to call them): text-based, or graphically.
Although the text-based way isn't necessarily the most friendly-looking way, you may find yourself preferring it. What you have to do is open up a terminal emulator (like Konsole, Gnome-Terminal, xterm, etc.) and make yourself root by typing
Don't type the dollar sign, that just represents the user prompt. Once you type "su" you will be prompted for a password, and in there, put in the password that you set up during the installation/setup process (for root, not your user). There are two commands you can use to install packages from the command line: rpm
Use the RPM command for when you have downloaded an RPM package, and use URPMI (which you will more than likely need to update) for installing packages from a repository (noun. a remote place where a whole lot of packages are available).
# rpm -Uvh package-name-version.architecture.rpm
# urpmi package-name
# rpm -e package-name
# urpme package-name
Graphically installing packages is made REALLY easy with Mandriva. I can't remember exactly where to find the MCC (Mandriva Control Centre) but if you search through the menus under "System" submenus, you should find it no problem.
It's really straight-forward from there.