Well, first, Apple removes previous versions of OS X from the App Store when it releases the next version. So 10.8 Mountain Lion is no longer available on the store. However, I've heard reports that you can call Apple and purchase a redemption code over the phone, which will allow to to upgrade to that version of OS X.
Next, you should make sure your Mac can physically handle the upgrade. Check the model number of your Mac (from the Apple menu, About This Mac, More Info; look for the hardware number - eg iMac8,1) and find out how much RAM you have (from that first About This Mac screen). 4GB or above is recommended if you can install it in your model - the more the better. Make sure you have sufficient hard drive space (if your HD has less than 10% available, I'd worry.)
Finally, make sure any applications you run are compatible with the upgrade. Notably, Office 2004 and older versions of Quicken got knocked out by 10.7 and 10.8.
Matt