Money: where to change it, and how far a card goes

South Korea is almost fully cashless. Even if you buy a 1,000-won item at a convenience store, you pay by card. There's no need to exchange large amounts of cash.
Airport exchange counters are convenient but have the worst exchange rates. The rates at private exchange offices in the city, especially around Myeongdong, are more favorable.
To withdraw foreign currency at an ATM, look for a machine marked 'Global' or with a foreign card symbol. Most ATMs inside convenience stores accept this.
When paying, if you're asked whether to settle in won or your home currency, choose won. Paying in your home currency applies the merchant's exchange rate.
There are still places where cash is necessary: traditional market stalls, old restaurants, and some food carts. Carrying around 50,000 won or so gives you peace of mind.
Tipping is not mandatory. Whether at a restaurant or in a taxi, you only need to pay the stated amount, and you don't have to calculate what percentage to add on.