The easiest approach is by train. The Southern Railway Line from Bangkok's Hua Lamphong or Bang Sue stations stops at Kui Buri railway station; several trains per day make this journey (roughly 3.5 to 4.5 hours depending on train class). The express trains are considerably faster than the ordinary services; check the State Railway of Thailand timetable before travelling.
By bus, take an air-conditioned bus from Bangkok's Southern Bus Terminal toward Prachuap Khiri Khan and ask to be dropped at the Kui Buri junction. Minivans also run from Hua Hin to Kui Buri. Driving from Bangkok takes about 3.5 hours on Highway 4 south through Petchaburi and Hua Hin.
There is no public transport from Kui Buri town to the national park; motorcycle taxis and occasional songthaews cover the route, or the park runs its own transfer from town during busy periods.