Kaesong is about 160km south of Pyongyang by road, and virtually all visitors arrive as part of a guided tour from the capital. Independent travel to Kaesong is not permitted — North Korea requires foreign visitors to travel with government-assigned guides at all times, and tour operators handle all logistics.
The drive from Pyongyang takes roughly two hours on the main southern highway. Most tours include Kaesong as a day trip, though overnight stays at the Kaesong Folk Hotel — a converted traditional Korean courtyard complex — are possible on some itineraries. If you have the option, staying overnight is worth it: the city has a different character in the evening when the tour buses have gone.
There is a rail link between Pyongyang and Kaesong, but it is not accessible to foreign tourists.