How do I upgrade OS X 10.5.8 to OS X Snow Leopard 10.6.8?

http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard

Choose About this Mac from the Apple menu and check the processor.

If it's a PowerPC Mac, it's already running the newest OS it can.

If it's an Intel Mac, click here, install the DVD, and run Software Update.

If you upgrade the OS, back up the computer first.

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Buy the upgrade DVD and follow the instructions, the DVD is availalbe directly from Apple's online store. It's really that simple.You can find the system requirements at:

• An Intel Core 2 Duo, Core i3, Core i5, Core i7, or Xeon processor
• Mac OS X v10.6.6 or later to install via the Mac App Store (v10.6.8 recommended); you can install without Mac OS X v10.6 by using an OS X Lion USB Thumb Drive, available on the Apple Online Store
• 7 GB of available disk space
• 2 GB of RAM

If your Mac is an Intel CPU based Mac, then you must purchase, from Apple, a retail install disc of OS X 10.6.3 Snow Leopard.

Found Here.

http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard

Then you use OS X Software update feature to update to OS X 10.6.8.

Make sure you backup up your entire system and important data befor embarking on a major systems' upgrade.