The way you are supposed to eat Korean barbecue is to build a bite sized wrap, also known as "a ssam" by placing the grilled meat, rice and your choice of banchan, "side dishes" such as garlic and Kimchi into a whole lettuce or perilla leaf and then fold and eat the wrap in one go.
You should also use separate tongs for raw meat and cooked meat so that you prevent cross contamination and use the provided scissors to cut larger, fully cooked pieces of meat into smaller portions before assemble the wrap.
Although you can also eat the Korean barbecue any way that you like but the above away is how Koreans traditionally eat barbecue.
While not required, Koreans will also often wear gloves when eating foods like barbecue and other greasy and messy foods to prevent their hands from becoming greasy, or sticky and messy from sauces and oils.
The gloves that Koreans wear while eating are often disposable gloves and either fit over both of their hands or are short, two finger protector type gloves that are called finger naps, for cleanliness and convenience.
The gloves that Koreans wear while eating, keep the Koreans hands clean from sticky, oily or saucy foods.
And the gloves also offer some minor protection from hot foods or hot surfaces, like a hot slab of meat, allowing for easier handling of the hot foods.
And the gloves that Koreans wear while eating also preserves grip and helps the Koreans maintain a better grip on their food item, especially when eating very oily foods.
Disposable plastic gloves are provided to people in many Korean restaurants for eating foods like fried chicken, pork ribs or any other oily or greasy or hot foods.
Two finger gloves also called "finger naps" are also used and available in many Korean restaurants and are smaller, special gloves which cover the thumb and index finger and are often used for eating foods such as burgers and pizza.
Koreans also consider it uncouth to lick your fingers or even blow your nose, especially when eating and if you use a toothpick you should also cover your mouth while using a toothpick in Korea.