First of all, you'll need an account on the Japanese Hangame site; so read up on the Hangame registration guide.
Second, log into your account and head over to the Goldwing site. Click the large button below the jet image on the top left corner (it contains a little red biplane and the word GO!).
Third, click ok when it prompts you for the download location; it'll download the Goldwing installer, it's less than 5MB.
Fourth, the Goldwing launcher will appear, and automatically start downloading after it prompts you a final time. When it's completed, you'll see the image to the right, simply click the bigger button in the bottom right corner (the one not surrounded in black) and the game will begin.
So long as your firewall is configured correctly everything should run fine.
Note that you must go to the website, be logged in and click the GO! image to be able to play.