What would be required for an undergraduate graphic designer to go into the field of game design?

I am finishing up my undergrad in graphic design and I am interested in learning more about game design. Possibly a Masters Degree. What should be the first step in the exploration process?

I know one of the requirements ultimately is drawing. Does anyone know of a great self taught book to improve skills?

The first step in the exploration process would be to View Forum FAQ (above).
Then read these:
http://www.sloperama.com/advice/lesson41.htm
http://www.igda.org/games-game-april-2006
Drawing is not a requirement for game designers. I'm surprised that as a graphic design major you'd be expressing concern about that.

You could be right about some students, but a lot of them are just studying because they don't know what else to do and don't want to work yet. Even in university/master's. At least that's how it is where I come from. History is a popular choice for those students.

In which case continuing their education would be a really smart thing to do. It keeps them off the streets for a few years and exposes them to a host of information and experiences they would not otherwise have. During that time they may discover something they are passionate about and may mature enough to make difficult life choices. Dropping out of school because you don't know what you want to do would definitely be the dumb option.

I was surprised to see this post is now being pinned as reference.
In all regards, I'll give an overdue update on my status.
I have now achieved over 6 months as a Project Coordinator.
I am still working on my side project which should hit online distribution platforms in Q1 2013.
If I'm lucky enough, I should be able to land in a job in Game Design after that.