Karakorum (the modern town is officially called Kharkhorin) sits about 370km southwest of Ulaanbaatar along a fully paved road. The drive takes roughly five to six hours in a private vehicle or jeep — longer if you stop, which you should.
Shared minivans depart from Ulaanbaatar's Dragon Bus Terminal most mornings when full. The fare is cheap and the journey is an experience in itself, crossing the broad Mongolian steppe. Seats fill quickly in summer, so arrive early. The return trip can require some patience; ask at your ger camp or guesthouse the evening before.
Most visitors come as part of an organised tour, which is also sensible: a driver and guide adds context to the ruins and handles logistics across a landscape where road signs are sparse and fuel stations scarcer. Multi-day circuits of the Orkhon Valley typically include Karakorum as a centrepiece stop.