Updated Oct. 4th, 2016. Credit to Jaisohn for optimizing.
Method 1: More Prep, Faster setup.
PREPARE the following in advance:
1. Prepare cash for your pc seat. Most PC bangs do not accept credit cards. 10,000 won should be more than enough.
2. A USB drive compatible with Windows with the following:
a. Melee v1.02 iso. (Most important, the rest you can download pretty quickly. I assume you own a copy of Melee.)
b. Dolphin 4.0-7840 (Our standard in Korea as of now).
ii. Make sure you are aware of the required netplay settings. Guide.
iii. You can save time setting Dolphin up by copying your settings folder as well. By default, this is saved in [user profile]/My Documents/Dolphin Emulator. More info.
c. Visual C++ install executable. Download the x64 version from here.
d. Driver for your GameCube controller. Zadig works with the Wii U and Mayflash adaptors.
3. Your controller and adapter.
AT the PC Bang:
If you've set up netplay before, it should be clear what to do.
4. Install Visual C++, Zadig. Set up Zadig: Guide.
5. Copy paste Dolphin and the Melee iso to the Desktop or wherever. Extract if necessary. If applicable copy-paste your Dolphin settings to My Documents (Should be 내 문서 in Korean). If you don't have that ready, set up Dolphin for netplay as shown in the guide. Make sure your controller works.
You are now ready to play Netplay. With LAN you should have around 1 ms ping, which is virtually lagless. Find a PC bang with lagless monitors (there are some with BenQ or CRT monitors) and you are all set!
Method 2: Slower, but Less Prep:
Do the same as above but download your the files at the PC bang rather than preparing a USB stick. This will take more time as you'll need to download everything, but other than the iso it's not that bad.
Brawl
Melee
Project+
RPS
Sm4sh 3DS
Sm4sh Wii U
Smash 64
SSF2
Ultimate