Penang is a busy international hub, so there are a lot of ways to get there.
Air travel is the natural choice to get to Penang. The national carrier, Malaysia Air System, flies between Kuala Lumpur and Penang. Thai and Singapore airlines also offer direct flights from their respective countries. For more information about the airport and airlines, see the Asia Airports guide to Penang International Airport. See the airport transfers page for information about getting from the airport to Georgetown.
Penang is easily reached by train from either Singapore via Kuala Lumpur or Thailand. Malaysian Rail has daily trains traveling up and down the entire length of the peninsula. Trains arrive in Butterworth on the mainland and it's just a short ferry ride across to Georgetown.
Traveling by bus is not something that readily comes to mind, but there are some excellent services around Malaysia that offer a level of comfort that can even out-do first class air flight. Check out Plus Liner for more information.
In addition to the mainland just minutes away, you can also get to Penang by ferry from Langkawi (about two hours) and Medan in Indonesia (up to six hours). Both of these services dock at the pier next to Fort Cornwallis.