How do I obtain iPhoto for a second-hand Mac Air? I obtained a Mac Air from a friend, second-hand. He restored a clean install of the OS, without the free Apps (iPhoto, iMovie…). These apps were included in the original purchase. We understood that it would be a simple matter of downloading these apps afresh from the Appstore. However, I am required to pay for them. I use my Appstore login, of course, not my friend's.

I guess one way to get these apps is to go and visit my friend and ask him to log in to the Appstore under his identity, but I would prefer to download these myself. I also suspect that this method may cause problems for a number of reasons: the device is now linked to my login, he probably already has his quota of devices linked.
The only legal way to transfer the iLife applications from him to you would be if he had the original iLife installation DVD that used to ship with new Macs. Being that it's an Air, and doesn't have a DVD slot on it, it's unlikely he still has that media.

Unfortunately, you're stuck with re-buying the iLife applications from the App Store using your own Apple ID. Using his App Store ID to put the software on your Mac and then switching the ID to your account would definitely be on the wrong side of Apple's terms of service.