I understand that this is a pretty basic question but I cannot find a direct answer anywhere. I have two computers running Snow Leopard: a Macbook Air (2011, pre-thunderbolt) and MacBook Pro 2009, which can both run Mountain Lion. According to my programmer / Apple friend, I can download Mountain Lion once from the App Store and use it to upgrade both machines. Is this true? I'm using one 'account' I guess but it's still two different machines, but my (trustworthy) friend was insistent I could. I can't find confirmation in any of the reading I've done here or on the Apple website.
You can install Mountain Lion on several Macs, provided that you use the same Apple ID for downloading it on them.
The Mountain Lion License Agreement explicitly says:
You can read the license by clicking the Terms and Conditions link at the bottom of the App Store window (left of the FAQ currently) and searching the license for the words "product usage" (presuming your store's terms are in english).
There are two different questions embedded in your question.
One is about license: If you purchase Mountain Lion, how many machines are you licensed to install it on.
The second is about the actual file you download: how many times can you use it without having to download again.
Perhaps surprisingly, the answer to the first is simpler than the answer to the second. You are allowed, as the license says, to install Mountain Lion "directly on each Apple-branded computer running OS X Lion or OS X Snow Leopard (“Mac computer”) that you own or control."
Can you do this without re-downloading the (rather large) file?
You need to download the Mountain Lion installer, then make a copy of the installer onto some external media before installing the operating system. The installation procedure will, by default, delete the install file once it is done, meaning that you can download it from the store again without buying another copy, but unless you copy the file before installing, you can only use the downloaded installer once (a rather frustrating experience, given how long it takes to download).
Yes you can. The way I did it was simpler than some suggestions imply. I purchased it and directly downloaded it to one computer. Then when it came time to download and install on a second, I just went into the Mac app store the same way , clicked download. It says it is $19.99, but once you click to purchase and enter your apple ID, as long as you have already bought it on another computer under that Apple ID, it then gives you a message saying such, and that the download is free.