10.5 Leopard discs don't require a serial number or 'key', but they are subject to the one per computer license agreement, or 5 for a family pack.
Just put the CD in to your computer, restart the machine, hold 'C' straight after you hear it chime and then it will walk you through the installation.
If you're upgrading from 10.4 I'd recommend doing an 'Archive and Install' which is under the 'customisation' tab on installation options.
This will keep all your files and user accounts etc (as long as you choose to retain them) and install a fresh OS for you.