Korea Local BestieTaxi cardworks offline once loadedType your destination. You get it in big Korean letters with "please take me here", so the driver can put it straight into navigation. Works for Kakao T too.
Download Kakao T, set it to English, type the destination, and the driver already knows where you're going. Pay in-app with a foreign card or in cash to the driver. Street hailing works too, but the app removes every language problem.
Regular taxis (orange, white, silver) all charge the same metered fare. Black "모범" taxis and the big vans are a premium service at roughly double. Not a scam, just a different product.
Every taxi takes cards and transit cards; say "카드 돼요?" and tap the reader in the back. Tipping doesn't exist; drivers will chase you down the street to return a 1,000-won note.
Many taxis have an automatic rear door. Either way, close it gently; a slammed door is the one thing that upsets Seoul drivers.
Between 23:00 and 02:00 fares are 40% higher by law, not by trickery. A refused short ride late on a Friday is common and legal to complain about; Kakao T avoids the problem.
Incheon to central Seoul is about ₩60,000–80,000 (more at night, plus the ₩6,600 toll). The train (AREX) is ₩5,000–13,000. Taxi makes sense only with big luggage or three people.
Pay by card and the receipt has the taxi's number. Call 1330 (tourist helpline, English) or the Seoul taxi lost-and-found via 120 (dasan call center). Kakao T rides can be traced in the app.