Divination is learning to use your inner eye
and use various objects to predict the future.
 You must have the Sight, because books can't
teach the subjet.  The course covers reading
tea leaves, palmistry, crystal balls, astrology,
and more.  Divination is started in the third
year of study at Hogswart. The first term
is devoted to reading tea leaves.  In the second
term palmistry is studied.

"Many witches and wizards, talented though
they are in the area of loud bangs and
smells and sudden disappearings, are yet
unable penetrate the veiled mysteries of
the future," Professor Trelawney went
on, her enormous, gleaming eyes moving
from face to nervous face. It is a Gift
granted to few."
Sibyll Trelawney

Diviniation was taught at the top of the
North Tower.  At the top of the steps there
was a  tiny landing, where there were no doors,
but there was a circular trapdoor in the
ceiling with a brass plaque that read,
"Sibyll Trelawney, Divination teacher."
Students ascended on a silvery ladder into
 a classroom that looked like a cross between
an attic and an old-fashioned tea shop.
At least twenty small, circular tables were
crammed inside it, all surrounded by chintz
armchairs and fat little poufs. Everything
was fit with a dim, crimson fight;
the curtains at the windows were all closed,
and the many lamps were draped with
dark red scarves. It was stiflingly warm,
and the fire that was burning under the crowded
mantelpiece was giving off a heavy, sickly sort
of perfume as it heated a large copper kettle.
The shelves running around the circular walls
were crammed with dusty-looking feathers, stubs
of candles, many packs of tattered playing cards,
countless silvery crystal balls, and a huge array
of teacups.

The textbook for this class is
Unfogging the Future by Cassandra Vablatsky
and can be purchased at
Flourish and Blotts in Diagon Alley.
Other Books About Divination
Broken Balls: When Fortunes Turn Foul
Death Omens: What To Do When You
Know The Worst Is Coming
Predicting the Unpredictable:
Insulate Yourself Against Shocks