Can I download Mountain Lion from the App Store and install it on my machine later? I have a very slow Internet connection at home, but I am traveling with my MacBook now and have temporary access to a faster connection. I'd like to take advantage of the fast connection to download Mountain Lion, but I don't want to install it until I return home and make a backup of the machine first.
Yes, the App store downloads an installer for Mountain Lion and stores it in the usual spot - /Applications.
You should only need a network connection after installing to get updates, etc.. and not to run the installer outright.
Be aware that the installation process deletes the installer once you are done installing the OS, so you might make a backup copy of the Install OS X Mountain Lion program before you run it.
There are a few complications to be aware of, and I think Apple is tweaking the download behavior. The answer above only works if you're an Administrator user, you haven't downloaded ML before, and you don't have an old copy of your install file in reach of Spotlight.
Also the download from App Store launches installer, so you have to quit to save it.
The best description of how to do this that I've found is here:
Briefly (I'll do a blog post on this):