Bus:The bus lines in Suwon are reliable and cheap. Most major stops have a listing of available bus lines with route information. While mainly listed in Korean, most major stops and points of interest are also listed in English.
Taxi:Taxis are prevalent in Suwon, and easy to use. Several offer "free translation" services. You should know a major feature near your destination as the Taxi drivers may not know specific addresses or minor building names, however with a little patience and understanding you will find a taxi willing to get you near your destination. Some will even call "English speaking" friends or relatives to help. Taxis are easily identified, mainly gray, white or black with lighted signs on top and in the front windows. Black Taxis are "luxury" taxis, tend to be more comfortable/larger cars, go slower, and cost more. The Gray or white taxis tend to get you there faster and cheaper, but my induce a bit more white knuckles. It is highly recommended to buckle your safety belt.
Subway: There are currently 4 stops that service the Suwon area. Suwon Station is the central, and largest in Suwon, and the second largest in the country, and also houses the train station proper, where you can catch a train to nearly anywhere else in the country. Seryu, Hwaseo, and Sungkyunkwan University are the others. There is currently another subway line under construction to service other parts of the city.
Walking: Suwon is a large city, but walking can be a nice alternative to the frenetic pace of Taxis and busses. There are few large hills in Suwon and wide sidewalks. Several walking paths provide 'short cuts' that driving may not.
Bicycle: Bicycling in Suwon is easy as the sidewalks are wide and many are combination sidewalk and bike path. There are only a few challenging hills in Suwon and pedestrian traffic is not congestive in most areas.