"‘I’ll read the leaves, if you want,’ said Miss Spink to Coraline. ‘Sorry?’ said Coraline. ‘The tea leaves, dear. I’ll read your future.’ "

The divining of your fortune with tea leaves is known as tasseography, people also perform it with coffee grounds and wine sediment.  The person reading your fortune looks at shapes left in the tea leaves at the bottom of the cup, after the tea has been drunk.  They interpret these shapes according to a standard symbolism, for example, seeing the shape of a snake would suggest that someone is feeling hostile towards the tea drinker, the symbol of a mountain would suggest something hindering the person.

Source

http://en.wikipedia.org/wiki/Tasseography