There are daily flights and boats from Athens which is very convinent and comfortable. Flights take around 35 minutes while boats take 4-5 hours to reach Mykonos.
All the major airlines fly from New Delhi, Mumbai, Bangalore, Hyderabad, Chennai, Pune to Athens. From there, you can either take a boat of board another plane to fly to Mykonos.
There are daily flights from Athens airport by Olympic Air and Aegean Airlines. From May till October charter airlines fly directly to Mykonos from many European airports.
From the mainlands of Greece, there are daily ferries and highspeed moterboats for Mykonos starting from EUR 32. The boats operate from Piraeus and Rafina.
On Mykonos you can get around by bus, taxi, car, scooter, ATV or boat. Bus serives are good and punctual. Taxis are very less in number and you will have to wait to get one. MOst popular mode of transportation to get around the island is to rent a bike.