1. By Plane
2. By Bus
Overnight buses run between Antalya and Nevşehir, a 9-10 hour journey. From Nevşehir, you continue to your Cappadocian town by shuttle minibus (servis). You might also decide to take a bus to Konya, see the sights there, spend the night, and continue to your destination the next day. Here's how to buy bus tickets in Turkey.
3. By Car
It's an interesting ride, along the ancient Silk Road past the Sultanhanı and other Seljuk Turkish caravanserais to Konya (good for a meal or overnight stop), then through mountain country down to the Mediterranean coast.
Remember that rental/hired cars not returned to where you rented them are subject to a return fee, which can be substantial, to get the car back to where it was rented.
Check with one of my recommended travel agencies for flight reservations between Antalya and Cappadocia.