The secret is to butterfly the rib to that you get a thin strip of meat with the bone on one end. Now depending on the thickness of the ribs you intend to use you can do either the one cut or the three cut method. The one cut method is done by laying the rib on its side and cutting down most of the way through the meat. Then you can fold open the rib making two equal halves that will cook much faster. If the ribs you intend to use are thicker you might want to go with the three cut method. The whole idea is to get an even thickness about 1/2 to 1/4 of and inch thick.
The three fold cut can be a little tricky so take the first one slow and you'll catch on. Place the rib on its side and cut down on the side away from the bone. Cut almost all the way through, leaving enough meat to hold it together. Turn it over and cut down right in the middle almost to the bottom. Turn again and cut along the inside of the bone. Done right you can open the rib up into a thin flat piece of meat that will grill up in minutes and not have the long connective tissue ruining the meal.
Once you have the ribs butterflied you are ready to marinate the ribs. The typical Korean marinade has soy sauce, ginger, something sweet like honey or sugar and some simple seasonings. The marinade should also contain some kind of vinegar or alcohol to tenderize the meat and carry the flavors deep inside. Because of the large surface area and the thinness of the meat you don't have to marinate for too long. One to two hours in the marinade is perfect.
Now it is time to grill. You want to expose as much of the meat to high, direct heat as possible. Korean style ribs should be grilled in a few minutes. Lay the ribs out on the grill and close the lid. Give them about 5 minutes then flip. What you are really doing is giving the meat a good sear and then flipping. Korean ribs should be cooked about medium.
In Korean you will find that the meat gets cut quickly into bite sized pieces with kitchen shears or just plain scissors. It might sound a little strange but it works.
You can serve these on rice or more traditionally with lettuce leaves, garlic, and some kind of hot sauce to make little beef lettuce wraps.