The climax of the book is when Santiago is captured, turns himself into the wind, and escapes. In order to become the wind, Santiago must incorporate everything that he has previously learned while on his journey.
The falling action comes next. After escaping, Santiago is able to make his way to the pyramids where he believes the treasure will be. Unfortunately, Santiago is attacked (again). All of his money is taken, and he is left with nothing. The only bright spot is that he overhears his attackers talking about a treasure in a church in Spain. Santiago must return to where his journey began.
The final resolution of the story is that Santiago returns to Spain and finds the treasure. He then plans to return to Fatima.
The climax of The Alchemist takes place when our protagonist learns to turn himself into the wind. In order to do this he must use all that he has learned about the interconnectedness of the universe.
The resolution takes place when he finally finds his treasure, and completes his journey (both physically and spiritually).
Of course this is an overly-simplistic explanation, but there is a great deal of depth to this book and an answer short enough for this format would certainly not do Coelho justice.
I see that you are a teacher. E-notes has some excellent resources for teaching this book.