Watch Swimming to Cambodia and then read Sex and Death to the Age 14.
You've got to start by seeing his performance. Gray was captivating on stage, and one of his major contributions is transforming the stage into a conversation (albeit a monologue) from behind a desk. Swimming is Gray storytelling at it's finest. The production does a remarkable job of channeling the energy and presence that Spalding brought to his live perfomance. Jonathan Demme directs (that same hand that powered Stop Making Sense) and Laurie Anderson adds sound effects to the drama.
Once you've gotten a feel for his voice, cadence and temperment, dive into texts of the earlier monologues. Sex and Death is a collection of five brilliant and well-edited pieces collected in an inexpensive edition. I can't say enough about the range of feeling and humor in these. There used to be a recording but it's long out-of-print. If any one from Random House is reading this, I'd be happy to buy the rights and distribute it.
From there, I think watching Gray's Anatomy or reading Impossible Vacation might be good choices.
(purchase) Swimming to Cambodia (DVD ~$25)
(purchase) Sex & Death to the Age 14 (Book $5 to $19)