Two things surprise most visitors: you pay at the counter, and you do not tip.
Korea has no tipping culture in restaurants, taxis, hotels or bars. Prices are inclusive and staff are not paid on the assumption of tips. Leaving money is not read as generous but as confusing, and staff will often try to return it. The exception is a small number of hotels and Western-style venues that add a service charge to the bill itself.
In almost all Korean restaurants the bill is settled at the register near the entrance, not at the table. Table service payment exists in cafés and upmarket restaurants but is the exception. If a slip of paper was placed on your table when the food arrived, bring it with you.
Splitting (더치페이, 'Dutch pay') is completely normal among friends and colleagues, and counter staff will split a bill across several cards without comment. In more traditional settings the most senior person may insist on paying for everyone — accepting is the polite response, not fighting over it.
Restaurant meals are not eligible for the tourist VAT refund, which applies to goods, not services. Do not spend time collecting restaurant receipts for that purpose. Shops displaying a Tax Free sign issue refund slips for purchases above the minimum amount.