The nearest airport is at Incheon, and there's a limousine bus from there to Suwon (in front of gate 7A, or at bus stop 3 or 12). The ride from the airport takes about 90 minutes and costs about W14,000. The limousine buses run daily every 15 to 20 minutes starting at 6:30am until 10pm. Suwon is also on the KTX railway line (from Seoul to Busan) and a ticket costs about W8,500 from Seoul. The regular train to Suwon costs W3,100 for a reserved seat and W2,600 for standing/unreserved seat. A cheaper alternative is to take the subway, line 1 (the dark blue one) from Seoul. It takes about an hour from the Seoul city center and drops you off at the Suwon central train station. It's a pleasant ride and costs about W1,500. You can also take express bus no. 7770 from Sadang Station, no. 3000 from Gangnam Station, or no. 900 from Guro Station. All three buses arrive at Suwon Station.
When leaving Suwon, the most number of options are available at the main train/subway station. Many Korail trains stop at Suwon on the way to several other destinations. The main subway access area is at the lower-ground-floor level, while Korail services are on the upper level. The ticket windows for regular trains are to the left of the escalators and there's a special window just for tickets to Seoul at the far left end of the windows. Station announcements are made in both English and Korean. Just remember to line up by the correct platform for your train, as passengers are allowed access to the platform only a few minutes before the train arrives.
There is a queue for taxis right in front of the station, as well as less expensive local buses (although the stop names are only in Korean). Express buses (more expensive, but with fewer stops) will have certain tourist destinations written in English.
There is also a free shuttle bus from Suwon Station to the Korean Folk Village. You can purchase an admission ticket to the folk village at the tourist booth, to the left when you exit the main station. You can board the shuttle bus near the car park. It takes about 30 to 40 minutes and brings you to the main entrance of the village.
There is a tourist information booth just outside of Suwon subway/train station (when you exit the main doors, go left) (tel. 031/249-5146), one at the Korean Folk Village (tel. 031/287-1332), and an info booth at Hwaseong Fortress (tel. 031/228-4677). The official Suwon website is at http://eng.suwon.ne.kr or call tel. 031/256-8300.