Upgrade to Snow Leopard, then update to 10.6.8
Snow Leopard Purchase
Check that your computer is compatible with Mountain Lion.
To check the model number hold down the option/alt key, go to the Apple menu and select System Information.
- MacBook (Late 2008 Aluminum, or Early 2009 or newer) model number 5,1 or higher
- MacBook Pro (Mid/Late 2007 or newer) model number 3,1 or higher
- MacBook Air (Late 2008 or newer) model number 2,1 or higher
Your Mac needs:
- OS X v10.6.8 or OS X Lion already installed
- 2 GB or more of memory (More is better)
- 8 GB or more of available space
Check to make sure your applications are compatible. PowerPC applications are no longer supported. Application Compatibility
You can also check by going to the  menu, select About this Mac, click on More info…, then click System Report and select Software/Applications.
If you have applications that you want to use that aren’t compatible, you can retain Snow Leopard and create a new partition to install Mountain Lion on or you can run Snow Leopard server in a virtual mode.
If your computer isn't compatible, you might be able to upgrade to Lion. Computer Compatibility - Lion
If you can/do upgrade, I recommend you make a copy of the installer and move it out of your Applications folder. The installer self-destructs. The copy will keep you from having to download the installer again. You can make a bootable DVD/USB stick to install using this free program.
Bootable Drive DVD or USB Flash Drive – Lion Diskmaker
From Kappy
Install Mountain Lion Successfully from 10.6.8