Preliminary Step 1 - Backup
This is a no-brainer.  You'll want to backup everything just in case things go wrong or you want to revert back.  Besides, an operating system upgrade is a great time to reinforce the need to make backups.  Ensure that you backup the contents of your hard drive such as your iTunes library, iTunes playlists, iPhoto library, documents, movies, and so on.  The method of backup is totally up to you but some options include dumping these items to an external hard drive or to discs.  If you are a MobileMe subscriber, you have access to a free backup application called Backup that makes backups quite easy.  You can also use third-party applications to make backups.

Preliminary Step 2 - Repair Permissions (not needed if you choose Erase and Install option described later)
After you've made your backups you should run the Repair Permissions and Repair Disk options in the Mac OS X Disk Utility application.

Installation

Insert the Mac OS X Leopard installation DVD and double-click on the "Install Mac OS X" icon and then click on Restart.  The Mac OS X Installer will begin once your Mac restarts.  Another way to kick off the process is to insert the Leopard DVD in your Mac's drive DVD drive, restart your Mac, then hold down the "c" key as your Mac restarts.  Be patient as the installation program may take a moment to start.

Once the installer begins you will be shown several dialog boxes that will ask for things such as your operating language.  You will also have to agree to the user agreement before you can proceed.  You will also choose the hard disk where you want to install Mac OS X.

There are 3 basic options to upgrade to Leopard

• Simple Upgrade: This is the easiest option.  It will upgrade all of the relevant components of your Mac OS X software and preserve your personal files and most settings.
• Archive and Install: This option is a more safe option in case you want to revert back to your prior version.  The installer will save your existing Mac OS X system files into an "archive" (backup) and will then install Leopard into a new system folder.  Keep in mind that this option eats up a lot of disk space because you have essentially have two versions of Mac OS X installed.  One archived and one new.  You have the choice to automatically import your user details and settings into Leopard.  This is a easy way to avoid having to reconfigure application settings, Mail, and things such as printers.  
• Erase and Install: This is the longest and most involved option because it involves two distinct steps.  Step one is a complete erase of your Macintosh HD.  Step two is the installation of the new Mac OS X version.  After Leopard is installed you will need to manually place all your files (that you backed up!), you'll have to re-enter all of your account settings, and re-install software such as iLife.  So before choosing this option, make sure you have all your settings and installation programs for your other software.

Note that more advanced and experienced Mac users often install Mac OS X upgrades on an external drive and then boot off of it at a later step.  This guide will not cover those steps.

One piece of advice: BE PATIENT! The upgrade process takes time and depending on your upgrade option and the performance of your Mac, the process can take somewhere between 30 minutes to upwards of an hour and a half.   A step common to all installs is a sanity or integrity check.  The installer will check the Leopard install DVD and the hard drive for any issues before the installation actually begins.  If there is a problem with the DVD or hard drive you will need to address it before you will be able to proceed.

Subsequent high-level steps will include things such as:

• Preparing the Disk: Verifying Destination Volume - this checks that your Mac meets the system requirements for Leopard, has enough space on the hard drive, and so on
• Installation - this will depend on the upgrade option
• Optimizing System Performance - Mac OS X does some things in the background to get the software to work optimally and more efficiently.  Experienced Mac users know that a key action in this step is the prebinding of libraries
• Restart

The installer will go through several steps depending on the chosen upgrade option.  If you're like me, you'll be watching the install process aws it takes place.  Don't be alarmed if at times the install appears as though it is running slowly or stalls.  A lot of things are happening under the covers that you can't see or observe.

Leopard is Installed
After reboot, you are almost done.  You may or may not see the user login screen, you may be asked for personal information, asked to create a MobileMe account and so on.  Once again, this all depends on the type of upgrade that you just performed.

One Final Step - Software Update
You'll want to check if Apple has released any updates to Leopard since the installation DVD was created.  Simply run Software Update from the Apple Menu and click on "Software Update".  It's a good idea to install the updates that appear.

That's it!  You're ready to enjoy and experience the greatest release of Mac OS X to date.  Congratulations on your decision to upgrade to Leopard.  Have fun and remember Apple's slogan you now have "a new Mac on your Mac".

Comments and Additional Information
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Updates

• May 1, 2009 - content revision