You'll want a USB drive - the 2012 MacBook Air computers support USB3 which is faster than the older USB but also a little more expensive right now. I've used a number of 3rd party drives and I've been very happy with Iomega's portable drives though I really like to get my drives from OWC because I like the Elite Pro Mini case and I can select exactly which hard drive mechanism I want. The drawback of buying something like the Iomega external drive is that you don't know what mechanism is inside. The Elite Pro drive will be more expensive but it is also easy to remove the drive and replace it with a large (or faster) one if need be. I have enclosures from OWC that are 5 to 10 years old that have been reused again and again. In the long run that's saved me money.
Plug the drive in (reformat it using Disk Utility) and when you save your file the first time the file selector will show you both the internal drive and the external drive under Devices in the left side of the fileselector. Choose the external drive and the folder (if desired) and then save.