There website is in English, so you shouldn't have any problems navigating it. As you can see, the test is free, anonymous and rapid, but you need to call for a reservation.
Do you have sex? Me too. So that means you probably should get tested for HIV/AIDS regularly. Living in Korea, you might not know where to go... But I have a few tips for you!
One service readily available for foreigners is the Korea Federation for HIV/AIDS Prevention (KHAP). It's located near Gireum station on line 4.
The Ivan Stop HIV/AIDS Project (ISHAP) is located in Jongno, but I'm not certain whether or not foreigners can use their services; their website is only in Korean. A lot of my condoms, however, are provided by ISHAP, so I figured I should give them a shout out here.
I also want to mention the international clinic in Itaewon. They do full anonymous STD screenings (not only HIV/AIDS) but there full service costs more than 100,000 won. Check out their website.
Most big hospitals can do tests for HIV/AIDS, but they might not be anonymous...
English teachers in Korea all need to be tested for HIV/AIDS (but not entertainers?) and it is kind of looked at as a foreigner disease. The rate is low in Korea, but that doesn't mean you shouldn't be careful. Wrap up and get tested regularly guys.
If anyone knows of any anonymous testing sites outside of Seoul, please let me know so I can inform my readers. Talking about HIV/AIDS is kind of taboo here, but you obviously shouldn't let that get in the way of your own sexual health.
Note: If you are in the Itaewon area, KHAP and the Open Doors Community Church (ODCC) in Itaewon is offering anonymous and free HIV testing on Sunday, September 16th, 2012. You should reserve on their Facebook's event page so they can prepare the right amount of kits. That takes away some of the anonymity, unfortunately, but I imagine you could message Daniel Payne (head of ODCC) if you didn't want the group to see your attendance.