After I Order OS X mountain lion from the online store, where does it go?

The installer will be downloaded to your Applications folder.

It will be named, "Install OS X Mountain Lion."

You should have received two e-mails about the purchase, one with an attached PDF that contains a redemption code to use in the App Store, and the other with the password needed to unlock the PDF and get the redemption code. Once you have the code, you can launch the App Store, and look under Quick Links for "Redeem". After entering your code, you should be able to download ML. After the download is finished, the installer will launch. At this point, it is a good idea to QUIT the installer, and copy it to a safe location outside of your Applications folder. The installer application unhelpfully deletes itself after it finishes installing the OS, and having a backup of it is easier than doing another 5+ GB download.