Olympus is set back beneath the pines, above the sea, and on a mountain. The closest airport is Antalya Airport (ATY) which is 1 hour and 40 minutes (98 km) by car.
The most convenient way to travel there from the airport would be to arrange a private transfer from your accommodation. You may also take a minibus (also known as a dolmus) from the Antalya bus station to the "Olympus junction" off of the main road. From here, you will wait for a second minibus to bring you down the road to the town itself. If you do not wish to travel by minibus, there are two other options.