Starting with OS X Lion, once you download the installer and run it on your system, it will disappear from your Application folder and the only way you can get it back is by holding down the option key while repurchasing so it will re-download the file or you can restore the installer from your Time Machine backup if you have one. Below I will write on how to make your own Mountain Lion install DVD or USB drive the easy way using Lion Disk Maker. For the sake of this How To article, you are advised to burn the installer prior updating to Mountain Lion.
Introducing Lion Disk Maker.
According to its author Guillaume Gète, Lion Disk Maker is an application programmed with AppleScript that can be used with Mac OS X 10.6, 10.7 and OS X 10.8 to burn a DVD or build a bootable drive from Mac OS X Lion or OS X Mountain Lion Installation program. Once run, it will look for the OS X Install program with Spotlight and will then proposes to build a DVD or bootable install disk. This app is a donation-ware app from Serial Server.
To make this work, you will need a dual-layer writable DVD to make an Install DVD or at least an 8GB USB flash drive or memory card to make a bootable Install drive. It is always a good thing to format your drive before making it into a bootable drive. Make sure you have your Mountain Lion downloaded or stored in your Application folder as Lion Disk Maker will finds it and asks you what media type you want to use to create the install disk, then handles the rest.
Okay, you already downloaded Lion Disk Maker, now go ahead unzip it and run it.
Basically you just need to follow the instruction on the screen and let Lion Disk Maker take care of the rest. On a mac with USB 2.0 the process will take around 30 minutes and it should be faster if you are on a newer mac with USB 3.0.
By now you should have a working OS X Mountain Lion Install Disk thanks to Lion Disk Maker. If you like the app, consider making a donation to the Lion Disk Maker author to support his work.