How do I upgrade my macbook OS 10.5.8 to the higher versions, like OS 10.6.8?

Phone the online Apple Store, order a Mac OS X 10.6 DVD, install it, and run Software Update. Further upgrades are available in the Mac App Store but won't work on all Intel Macs.

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Start by checking if you can run Snow Leopard:

Requirements for OS X 10.6 'Snow Leopard'

http://support.apple.com/kb/SP575

Whilst Apple have withdrawn Snow Leopard from their stores, you can still get it from Apple by calling 1-800-MY-APPLE (if you are in the USA) and they will supply the SL DVD for $20 for a single user, or $30 for a family pack that covers up to 5 Macs. You can also purchase the code to use to download Lion from the same number (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:

http://www.apple.com/osx/specs/

If you are outside the US call your national Apple Helpline:

http://support.apple.com/kb/HE57

If you're in the UK, use this number: 0871 508 4400

When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.

To use iCloud you have to upgrade all the way to Mountain Lion:

http://support.apple.com/kb/HT4759

Snow Leopard will be a great improvement even if you cannot go any further.

Before you buy anything, first make sure your Mac is compatible.

To see how far you can go check the Minimum specs for Snow Leopard. Mac OS X v10.6 Snow Leopard -Read the Technical Specifications

Neil's detail covers North America but In Europe or otherwise to buy Snow Leopard … call your National Apple Helpline. Find it at … http://support.apple.com/kb/HE57