Malaysia Airlines, Jet Airways, Singapore Airlines, Cathay Pacific, Malindor Air are the carriers that will take you to Penang and then Georgetown, from Indian cities.
Air Asia has a lot of flights to Penang Airport. Flights land within Malaysia (Kuala Lumpur, Kuching Johor Bahru, Kota Kinabalu and Langkawi) as well as Singapore, Hong Kong, Indonesia (Jakarta, Medan, Surabaya) and Thailand (Bangkok).
You can take metered taxis or even rent a car from the airport, to take you to Georgetown.
Get into one of the buses from the Butterworth Bus Terminal. After that, you can take a car ferry to take you to the ferry terminal. If youêd like to take a bus directly to Penang Island, get into one that stops at Sungai Nibong station, close to Georgetown.
The ferries at Georgetown are very convenient for travelling. There are ferries going to and from Butterworth. You can alight at the port/stop and take a bus to your hotel.