The only road is an unpaved dirt road which is very bumpy at times, but nonetheless accessible by 2WD. For hints and tips, read Driving in Australia. Seeing the park and the lookout is an easy day trip from Oberon, slightly longer from the towns of the Blue Mountains such as Katoomba, and possible in a long day trip from Sydney. If you are visiting Jenolan Caves, the trip to the lookout will take around 30 minutes each way.
There is no public transport to the park. Driving is the usual way of getting there. It would be possible to cycle from Oberon if you were particularly enthusiastic.