Blackthrows (also known as kamikaze boxes, drop boxes or chaosboxen) are computers that no one know who owns them. They just sit somewhere and communicate with random computers at the internet. Because no one knows who owns them, the owners can do pretty much whatever they want with them. If there is networks surveillance in a country, the blackthrow could be used as an anonymizing proxy.
But how does one obtain a computer in such a way that no one knows who owns it?
The first method is the obvious one. One simply enters the corporate building at night and installs it somewhere, and makes sure that it has WLAN access (possibly requires that you crack the WLAN).
The second method is to simply buy one. In Sweden it is possible to buy anonymous credit cards at Seven Eleven and Pressbyrån. It is then very simple to just go to a VPS-hosting website and order a virtual machine under a false name (using TOR ofc.)
Setting up an OpenVPN server in a virtual machine in Hong Kong or somewhere else is then not too difficult. If you want absolute anonymity you could instead ssh (or telnet?) to it via I2P.
This wiki article at cryptoanarchy.org has more information about how to buy an anonymous VPS.