To reach Cappadocia from India, you'll have to take a flight to Istanbul. Direct flights from Mumbai and New Delhi are operated by Air India and Turkish Airlines. Flights from all other international airports have connecting routes to Istanbul. From there buses run regularly to Cappadocia.
Turkey suspended it's visa on arrival services in 2014, so now you have to apply for a Turkish visa. This can be done through the VFS Global website, by submitting photographs and the required documents at their visa centre. The list of requirements is provided by the Turkish embassy.
Kayseri is very well connected to the entire country via rail, and direct buses can be taken to Goreme and other places in the Cappadocia.