what do I need to do to upgrade from OsX 10.5.8 to Mountain Lion?

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OS X Mountain Lion system requirements

To install Mountain Lion, you need one of these Macs:

iMac (Mid 2007 or newer)

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

MacBook Pro (Mid/Late 2007 or newer)

MacBook Air (Late 2008 or newer)

Mac mini (Early 2009 or newer)

Mac Pro (Early 2008 or newer)

Xserve (Early 2009)

Your Mac needs:

OS X v10.6.8 or OS X Lion already installed

2 GB or more of memory

8 GB or more of available space