Flying to Penang
From outside Malaysia, fly to the Kuala Lumpur International Airport (KLIA) or straight to the Penang International Airport, on Penang Island. The airport is just 20 minutes from Georgetown.
There are several (almost hourly) daily flights from Kuala Lumpur and a number of flight from Johor, Langkawi, East Malaysia (Kuching, Sarawak and Kota Kinabalu, Sabah) and from Singapore to Penang. You can also transfer from any domestic destinations at KL to Penang.
Other connecting air flights available from Penang are to domestic airports are: Langkawi (Kedah), Kota Baru (Kelantan), Kuala Terengganu (Terrenggnu) and Kuantan (Pahang).

Penang International Airport - Penang International Airport is located at Bayan Lepas on the island of Penang. The best way to get to and out of the airport is by taxi or car as the airport is only about 20km from the city centr of George Town. Taxis, buses and limousines are available between the airport and various destinations on Penang Island.   Buses passes right at the doorstep of the airport, that take you to the city and also the ferry jetty terminal. Counters for taxis and car rentals are located at the arrival hall, to your right, after you pass the glass exit (after the custom check point). Taxis and limousines operate on a coupon system where fares are fixed according to the zone your destination is located.

Airlines flying to Penang

Airline/ Flights to Penang by  Malaysia Airlines, Air Asia (Low Cost carrier), Firefly (Low Cost flyer), Singapore Airlines, Silk Air, Xiamen Air, China Airlines, Thai International are some of the airlines flying into Penang.
Malaysia Airlines (MAS) has a number of daily flights to and from KLIA (Kuala Lumpur), Langkawi Island, Kuching, Kota Kinabalu. Direct International destinations by MAS to Penang are: Bangkok, Medan, Singapore, Hong Kong.
Air Asia flies to Penang from KLIA, Johor Bahru, Kuching, Kota Kinabalu. Direct international destinations are: Jarkarta, Medan, Macau, Hong Kong, Bangkok (also see: Thailand to Malaysia), Singapore
FireFly (MAS budget airlines) flies from Penang to Johor Bahru, Langkawi, Kuala Trengganu, Kota Bahru, Kuantan and KL (Subang), and international destinations such as Phuket, Bandar Acheh, Koh Samui and Singapore
JetStar flies from Singapore and Perth to Penang daily
Tiger Airways also flies from Singapore to Penang
Singapore Airlines (Singapore)/Silk Air flies daily from Singapore to Penang Island.

Singapore to Penang by low cost / budget carriers
Air Asia, Jetstar, Silkair and Tiger Airways are the budget carriers that have at least two flights a day from Singapore or KLIA to Penang International Airport. Prices are competitive and fares are very low during off-peak seasons (non-holiday periods or weekdays).
The best option is to fly direct to Penang daily from Singapore (Terminal 1 or budget terminal). Alternatively fly by Air Asia or FireFly (sub. of MAS) to Penang from Senai Airport, Johor Bahru (JB) - this route is frequented by those in JB and coming from Singapore. It is easy to get a taxi or bus from the JB to Singapore or vice versa. The second alternative is fly via KLIA. There are more flights available on the KLIA to Penang and Singapore-KLIA routes. To fly, fly Singapore to KLIA (LCC Terninal), check out and then check in (at the same terminal) to fly on a low cost carriers such as  Air Asia to Penang.
(Important note: Budget airlines are point to point air services, so be sure to have 3 hours interval between your flight schedule, if you have to board another flight.)
Note: Malaysia Airlines's budget airline based in Penang, called Firefly, flies to the island from  Phuket and Koh Samui, Thailand.