There are no direct flights or trains, so you’ll probably go by busor car.
You may find a direct bus all the way from Nevşehir(Cappadocia) to Denizli (for Pamukkale) or vice-versa, but it’s also possible you’ll have to change buses in Konya—not a big problem, but it adds some time to your trip. Try the Metro Turizm and Öz Elbistan Seyahat companies.
These buses depart in the evening and arrive the next morning, a journey of about 10 hours.
It’s 306 km (190 miles) east from Pamukkale to Konya through Turkey’s lake country, a drive of about 5 hours.
Stop at Eğirdir (eh-YEER-deer) for lunch, and enjoy the scenery around the lake of the same name.
Stay the night at Konya to see its great Seljuk Turkish buildings(especially the Mevlana [Rumi] Museum), then continue along the ancient Silk Road via Sultanhanı to Nevşehir, Cappadocia (221 km, 137 miles, 3 hours) on the next day.
For details, see my 5-Day Ephesus—Cappadocia Driving Itinerary.
Turkish Airlines has daily one-hour nonstop flights between Istanbul‘s Atatürk Airport and Denizli Airport (DNZ) in early morning and late evening—unfortunately, not the most convenient times to make connections to or from such places as Cappadocia.
Similarly, AnadoluJet and Pegasus Airlines have daily one-hour nonstop flights between Istanbul‘s Sabiha Gökçen Airport(SAW) and Denizli Airport (DNZ) at similarly less-than-convenient times for connections.