Flights from India to Italy are available from nearly all the international airports of the country. Airlines such as Qatar, Etihad, Air India, Jet Airways and many other airlines provide flights to Rome. Air India operates direct flights only from New Delhi and Bombay. From Rome, you can take a train to Pompeii, or rent a car, both of which will take you approximately 2 hours.
Pompeii does not have an airport. A flight has to be taken to Naples or Rome, and then a train or bus to reach Pompeii.
You can hire a car and drive down from neighbouring cities, but you will have to deal with the heavy traffic near the modern city of Pompeii. Parking can also be a hassle at times.
The rail would be the best way to reach Pompeii. You can get on the Circumvesuviana Napoli-Sorrento line from either Naples or Sorrento and get off at Pompeii Scavi. If you're coming from Rome, you can get on at the Termini station, the tickets costs around EUR 11. You can also get on a local train from Salerno. You can keep your bags at the station for a small fee. There is a Tourist Information Office close to the Pompeii Scavi station.
Bus services from Naples are organised by SITA. Buses run frequently and the route is quite nice. The cost is similar to the train ticket.
If you have taken a cruise, you can check if they will provide a hydrofoil boat transfer to Pompeii from the Bay of Naples. From the port at Pompeii, there will be a bus shuttle to the ruins.