Göreme has no airport or train station of its own. Most visitors arrive via one of two airports or by overnight bus from Istanbul.
By air: Kayseri Erkilet Airport (ASR) is the closer airport, about 75 km east. Direct flights from Istanbul (Turkish Airlines, Pegasus) take about 90 minutes. From the airport, shared airport shuttles (Havaş) and private transfers run to Göreme — shuttles are cheap but drop you at Nevşehir, from where you need a connection. A private transfer from Kayseri direct to Göreme costs around 30–40 USD and takes about an hour.
Nevşehir Kapadokya Airport (NAV), about 40 km from Göreme, has fewer flights but is sometimes cheaper and closer for western Cappadocia. Check both airports when booking.
By bus: Overnight coaches from Istanbul depart from the main Esenler otogar, operated by companies including Nevtur and Süha. The journey takes 9–10 hours and arrives in Nevşehir, from where free hotel-bound servis buses (run by the coach companies) take you to Göreme. Departures from Istanbul are typically in the early evening, arriving before dawn. This is the budget option and also avoids a wasted day of travel.
By bus from Ankara: Buses from Ankara take around 4–5 hours to Nevşehir. More frequent than Istanbul services and useful if you are already in central Anatolia.