http://doc.mandrivalinux.com/Mandrak.../Starter.html/
what format is the azureus file youve got?
what format is the java runtime environment you donwloaded?Does it have directions?Are you sure Mandriva didnt come with java already?(it should,but I wouldnt be shocked if it didnt)
When in doubt, always check the website where your distro came from, mandrake or mandriva its called nowadays has a decent website unlike many of the others.
software for linux comes in many forms, without details I can only make assumptions and guesses to help you
there's also whats called binaries, which are precompiled packages ready to be installed, theres also software that needs compiled first.
binaries come in all sorts of styles/formats, mandrake uses the rpm format,so does redhat and suse........files with an rpm suffix
if the mandrake web page tutorial leaves you lost, try here too and familiarize yourself with linux in general
http://www.lowfatlinux.com