Buses in Seoul are color coded and numbered. Yellow buses run within a local area. Blue buses run between multiple districts. Red buses run between cities (Seoul and Gyeonggi-Do).
Depending on where you want to go, a bus may be the fastest option. Moreover, if your location is not near a subway stop, you can probably find a bus that runs from the subway station to or near wherever you’re headed. If you used a T-Money card, this transfer will usually be free.
On this site, you can input your start and finish points, and it will determine the fastest method. You can also look up the routes of individual buses. The site is designed for internet explorer, and may not be compatible with other browsers.