How can I upgrade my OS 10. 4 to OS 10.5?

Typically by finding and acquiring an OS X or OS X Server 10.5 distribution on the used market, or by finding and purchasing a system already running OS X or OS X Server 10.5. If it's OS X client you're upgrading (as implied byu your reference to MacBook Pro), you'll need to find a retail copy — the system-specific disks weren't usually useful across different models — and if it's OS X Server (as implied by the forum this question was posted in), you'll also need a serial number. The disk you acquire will also need to be for PPC or Intel depending on which processor is in your system, as well.

As for the the literal question, make an external backup or two of your current disk using Disk Utility or some similar tool (as upgrades do occasionally fail), then boot from the 10.5 DVD, and follow the displayed directions.

There are often (always?) release notes for OS X or for OS X Server included on the DVD that you can access and read prior to performing the upgrade. Insert the DVD into the drive and use Finder to access the DVD.