WARNING: the following method does not work anymore, since Facebook closed this option in Aug 2019
Facebook has recently disabled the usual way of performing Graph searches, which worked by crafting URLs in the correct format. This strongly limited the capacity of researchers, journalists and investigators to make researches using Facebook data.
Soonafter, I published the tool fb-search, allowing users to easily perform searches.
Social Links also published an article that shows another way to perform some Graph searches, although cumbersome, since it consists of replacing some values in an http requests.
To demonstrate how this functionality can be used easily, I have built a Firefox extension that lets you perform several Graph searches using the above trick. You can find code and instructions here: github.com/sowdust/searchbook.
Disclaimer: make sure to read Facebook Terms of Service. All information and code are provided for educational purposes only. Using this code might be against Facebook Terms of Service or possibly even illegal. The authors are in no way responsible for any misuse of the information or the code provided.
Update: Searchbook now also works on Chrome too: https://github.com/sowdust/searchbook-chrome/