There is an airport on the southeastern tip of Penang, Penang International Airport, at the distance of 16 km from Georgetown.
I post the link to the airport here, and here I post the link to Wikipedia which has good information on the airport.
If you want to go by train to Penang, then you will have to search the trains for Butterworth and from there take the ferry to Georgetown. Remember to put "Sentral Kuala Lumpur" as origin, or destination if you are going to KL. Sentral is the main railway station.
You can also look at this pdf for times.
You find bus station underneath the KOMTAR complex.
One way of getting over to George Town from the mainland is driving across the Penang Bridge and i do personally consider the bridge an attraction aswell as something you can drive over as it's quite a pretty construction in my eyes.
The bridge is 13,5 kilometers long and it's a toll bridge so you need to pay to cross it, but the price is not very high.
Be aware though that pedestrians and bicycles are not allowed on the bridge though, so they will need to use the ferry when crossing.
The night train to Kuala Lumpur leaves Butterworth on the mainland at 11pm and arrives at 6.40am. The seats are comfortable but beware of the air conditioning, try to find some blankets or wear a coat, it is freezing.
It's an err.. um... interesting place to say the least.
The idea is that on the Lane signboards are the bus numbers that will arrive/ depart from that lane. Provided you know what bus number you want (any local will be able to help you there), the theory is that you wait in that lane and, sooner or later, your bus will arrive. Like I said, that's the theory.
In practice, some bus numbers go through this terminal at a much more frequent rate than others. Sometimes a backlog in buses occur as the ones that arrive first, don't seem to want to leave unless they have a full load. This creates havoc so the buses that are queued up in the street outside the terminal waiting to get it, randomly pick another empty lane and stop there. It can end up being like winning the lotto, trying to guess what lane your bus will turn up in. If it's not the one you're in, you'll get to play a game of Frogger, trying to cross lanes with buses transiting through at breakneck speed only to discover the bus leaving just as you get there!
Should you just miss the last bus and have to wait a while, there are toilets in the area and a newsagent stand with some food and water.
For those sensitive to pollution, you may want to find somewhere else to wait, as the carbon monoxide build up gets to shocking levels. There are exhaust fans in the roof, but most of the time they seem woefully inadequate.
pubic transport is still in a mess... though I'm wondering if the free circuit buses that go around the city centre are still running...
LATEST NEWS: Finally, we are going to get a so-called monorail system on the island to be build in the next 5 years! There will be some changes to the bus systems as well. Hope all will be good...
The ferry service connecting Penang to Butterworth runs every 20 minutes and takes 15-20 mins to reach the port. The ferry is basic yet efficient, it is certainly very popular and cheap.
There are hundreds of trishaw drivers plying the streets around Georgetown. It's a slow, but rather pleasant way to travel, provided the journey isn't too long.