Make sure you're within arm's reach of a hospital before doing this. There is only one entry to the drinking game...whenever the characters say "Escaflowne", or you hear "Escaflowne" chanted in the background music, take a drink. You'll be dead before episode three.
God help you if you try this whilst watching the Fox Kids version of the show (Some episodes can be found on Youtube). With all the flashbacks and background music changes, you're bound to hear "Escaflowne" pop up a lot. It's likely you might not even survive the opening theme, which chants "Escaflowne" FIFTEEN TIMES IN FOURTY-FIVE SECONDS!