How do I upgrade from Mac OS X 10.5.8 to Mountain Lionn

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Whilst Apple have withdrawn Snow Leopard from their stores, you can still get it from Apple by calling 1-800-MY-APPLE (if you are in the USA) and they will supply the SL DVD for $20 for a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

What is your Mac? Mountain Lion only works in:

iMac (Mid 2007 or newer)

MacBook (Late 2008 Aluminum, or Early 2009 or newer)

MacBook Pro (Mid/Late 2007 or newer)

Xserve (Early 2009)

MacBook Air (Late 2008 or newer)

Mac mini (Early 2009 or newer)

Mac Pro (Early 2008 or newer)

I have a iBook G4 and the latest OS X that support is Leopard 10.5.8.

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