Mountain Lion is not a freebie patch you can install thru Software Update. It is a full fledged operating system that costs $20 and can only be obtained thru the App Store application.
What? No App Store in your Applications Folder? Of course not, you have Leopard. So, you have to call Apple so they will sell you the 10.6 Snow Leopard Install DVD for $20. Then, when you have "updated" to that, you'll find the App Store in Applications and will be able to pay another $20 to download the Mountain Lion installer and complete the desired "update"
System Requirements for Mountain Lion:
Call Apple and buy OS X Snow Leopard for a fee.
Install it and update it through Software Update.
Once Snow Leopard is installed, you can go to App Store and buy and download
Mountain Lion. It costs $19.99.