In literature and film, there are various stages which reveal aspects of the work being analysed in terms of its dramatic structure. This structure ensures that the story flows and reaches a satisfactory ending. The introduction or exposition when the characters, setting and basic ideas of the story are introduced helps the audience or the reader to identify with the characters and accept and understand the story. As the story progresses the rising action becomes apparent as conflicts develop and complications arise which build towards a climax. There is often tension and excitement and, in terms of A Midsummer Night's Dream, certainly confusion.  The climax is the turning point in the story and the audience or reader ponders whether the main characters will succeed in their efforts or fail. 

In A Midsummer Night's Dream, the comedic effects of Puck's mischievous magic and the resultant series of unlikely love choices, mean that things at this point could go terribly wrong. The fate of the main characters lies in Puck's hands and he has the power to correct the effects of his love potion or to watch the lovers make mistakes and continue in their bewilderment. Towards the end of Act III, scene ii Helena refers to Hermia as "little but fierce" (325) and Hermia is incredulous at the events that are unfolding and Demetrius and Lysander have resolved to fight for Helena. Therefore, this is a turning point or climax and only intervention by Puck can resolve the conflict.   

The falling action will subsequently reveal how the conflict will be resolved and the resolution will ensure that things return to normal or, in A Midsummer Night's Dream, love will prevail and will resolve all the issues ensuring that all the characters are content with the result. 

I believe that the climax of the play comes in Act III, Scene 2, when the four lovers are at the height of their confusion.  Both Demetrius and Lysander are pursuing Helena, and both Helena and Hermia are amazed at this.  The guys go off to find a place to fight, and Hermia threatens Helena with a physical fight as well.  They all run off and Puck and Oberon are left to trick them into the right areas to sort it out.  The falling action begins in IV, 1 when Theseus and the other Athenians find the lovers in the woods and the triple marriage is set.  My opinion is based on the main plot of the four lovers.  If you focus on the Titania/Bottom subplot, the climax of that story comes in IV, 1, with Titania and Bottom at the height of their infatuation.  

The climax of A Midsummer Night's Dream is act 3, scene 2. The climax is the point at which all of the tension in a story culminates—when the drama gets most intense.

In act 3, scene 2 of this play, the four human lovers, Demetrius, Helena, Lysander, and Hermia, all confront one another. Oberon’s servant Puck was supposed to put a love potion into Demetrius’ eyes so he falls in love with Helena, but he accidentally put it in Lysander’s eyes. When Oberon realizes this, he puts the potion in Demetrius’s eyes. Because of this mix-up, both Demetrius and Lysander fall in love with Helena when they wake up.

The climax comes in this scene because now, both Demetrius and Lysander are chasing Helena around and she cannot understand why. She thinks they are making fun of her and it is all a big joke. Fed up with them all, she exclaims,

O spite! O hell! I see you all are bent

To set against me for your merriment.

Meanwhile, Hermia is very upset, because she cannot believe that Lysander is being mean to her. She and Lysander are in love with one another, so his sudden change in behavior shocks her. Hermia begins to fight with Helena, and Demetrius and Lysander are on the brink of physical confrontation.

Ripe with confusion, misunderstanding, and tension, this argument between all four of the lovers is definitely the most intense scene in the play. It all gets resolved at the end of the scene when Oberon has Puck separate the men and then puts a potion in Lysander’s eyes to counteract the other one. But despite the role that magic played in this confusion, Puck still makes an insightful observation in this scene when he sees Lysander pursuing Helena and says:

Lord, what fools these mortals be!

The climax of the story is the moment of crisis and the moment of greatest emotional intensity. It is also the point at which the crisis begins to be resolved but has not yet reached full resolution.

In A Midsummer Night's Dream, the crisis takes place the moment Oberon enchants Demetrius into falling in love with Helena. At the same time, Puck brings Helena back on stage with Lysander chasing after her, so that now both men are pursuing the same woman, which happens to be the opposite woman they were pursuing at the beginning of the story.

In this scene, Puck reaches a moment of emotional intensity because he finds it hilarious that both men are now pursuing the same woman and refers to all of the Athenians as fools. Also, he says that absurd things please him best, as we see in his lines:

Then will two at once woo one.
That must needs be sport alone;
And those things do best please me
That befall preposterously. (III.ii.119-122)

Also, enchanting the lovers creates a great deal of animosity amongst the Athenian characters. Instead of being overjoyed that two men now love her instead of none, Helena distrusts their sincerity and accuses both men of mocking her. Not only that, she accuses her best friend Hermia of being in on the joke. Since the mix up of the lovers causes so much animosity, we see that this is the most emotional part of the play.

We begin to see the resolution take place when Oberon gives Puck orders to stop the fight between the two men and make them follow him all over the forest until they drop from exhaustion so that both men can be enchanted with the love flower again and this time paired with the correct woman. 

How does A Midsummer Night's Dream end?

A Midsummer Night's Dream ends with the four human lovers, now properly sorted out, returning to Athens. Theseus finds their story improbable and thinks it must have been a dream. Hippolyta, however, finds it impossible they could have all had the same dream. Theseus allows the wedding of Hermia and Lysander to take place. The entire last act is a wedding celebration, primarily for Theseus and Hippolyta, but also for Hermia and Lysander and Helena and Demetrius.

Given several choices of entertainment, Theseus lets the mechanicals stage their version of Pyramus and Thisbe. Although the play is a tragedy, it takes on a festive and comic tone as the mechanicals overact, stop to address the audience, are spoken to by the audience, and in general show their incompetence. This performance provides lighthearted and zany entertainment.

At the very end, as night once again falls, the fairies take over the palace for their own celebration once the humans have gone. Titania and Oberon bless the marriages, promising the couples will be happy and will produce healthy children.

At the very end, Puck has the last word, addressing the audience with a choice: if they don't like or are offended by what they have just seen, they should simply treat it as a dream.

What is leading up to the climax in A Midsummer Night's Dream by Shakespeare?

The rising action of A Midsummer Night's Dream is pretty straightforward, though we follow three separate groups throughout the play. At the beginning we meet the lovers—Helena, Hermia, Lysander, and Demetrius. Helena is in love with Demetrius, who loves Hermia. Hermia loves Lysander and the two decide to run away together when Hermia's father tries to force her to marry Demetrius. Helena tells Demetrius that they're planning to run away, and when Demetrius chases after them in search of Hermia, Helena follows him. Then we meet the "rude mechanicals" as they prepare a play for Theseus' wedding. They plan to rehearse in the forest, where we also meet the fairies. The king and queen of the fairies are arguing over a child that the queen, Titania, has in her keeping. Oberon, the king of the fairies, wants the child for himself, but Titania refuses to give the boy up.

Oberon's sprite-like servant Puck sees the lovers running through the woods, chasing after one another—Hermia with two men on her trail, and Helena neglected. Puck and Oberon decide to intervene, but Puck mistakenly casts a spell on both Lysander and Demetrius, which makes them fall in love with Helena. Hermia, appalled at this, tries to persuade Lysander to come back to her. When he refuses, Hermia turns on Helena and they fight in the woods. Meanwhile, as the rude mechanicals rehearse in the forest, Puck casts a spell on their lead actor, Bottom, turning him into a donkey. He also casts a spell on Titania as she sleeps, and when she wakes she falls in love with Bottom. They dally away together. Eventually, all the lovers fall asleep in the forest, and Oberon and Puck decide to set things right. They leave Demetrius under the spell (that way he remains in love with Helena), but they return Lysander back to his former affection for Hermia.