Each proxy site is hosted online on a web server, it's a website and uses specific scripts that can hide the users IP and bypass those kind of web filters. There are different kinds of proxy scripts. The majority of those scripts are written in php which makes them even popular due to the popularity of php.
PHProxy Script is probably one of the most famous proxy scripts but its development has stopped for some years now.
Glype Proxy Script is by far the best proxy script between the rest till now. The script's development hasn't stopped till now as the team behind it supports it and improves it all the time.
Zelune Proxy Script has two different versions. One of it is hosted on Zelune.com and the other on Zelune.net. Both of those scripts are now under the same ownership which is Zelune.net. Unfortunately the development has stopped as they have moved to another proxy script the PhPhantom Proxy Script
Cgi Proxy Script is probably the oldest proxy script out there. The first version was released by James Marshall on August 3rd 1998.