Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Initial Situation
Hermia loves Lysander, Lysander loves Hermia, Demetrius loves Hermia, Helena loves Demetrius, and no one loves Helena. Oh, and Egeus wants his daughter killed if she doesn't follow his plan of marrying Demetrius.
About twenty lines into the play, we hear Egeus's complaint against his daughter Hermia, and we know the initial situation is a conflict itself. The play will definitely be about resolving this pickle.
Conflict
Titania and Oberon quarrel. Lysander and Hermia run off together and get lost in the woods, and Demetrius and Helena follow them.
Further conflict arises in yet another set of main characters: Oberon and Titania. The fairies' fight (over a relatively small thing) has very serious consequences on the entire natural world. In contrast, the young lovers are worried about a serious thing (love), but the way they deal with it only matters to themselves and their families. The scene is set for our Athenian heroes to get involved in this other conflict. As Titania and Oberon announce that the natural world is all mixed up, the four lovers go wandering into that very natural world, with predictably zany results. We're all set for the young Athenians' problems to become even more complicated, reflecting the conflict that brews in the wood around them.
Complication
Puck puts love potion on Lysander's eyes by accident, causing him to fall in love with Helena and forsake Hermia. Oberon enchants Demetrius and he too falls in love with Helena. Puck has turned Bottom's head into that of a donkey.
Puck's mistaken enchantment of Lysander further complicates an already difficult situation. True love has betrayed itself (Lysander leaves Hermia) and, with the addition of Demetrius's enchantment, false love appears to be true (Demetrius claims to love Helena). Now the pendulum has swung from loving Hermia to loving Helena. Elsewhere in the forest, Puck has interfered with the Mechanicals' rehearsal by transforming their main character into a beast and sending the others off screaming into the woods.
Climax
Lysander and Demetrius fight; Hermia and Helena fight.
This is an ugly resolution to the whole love-juice situation. Demetrius and Lysander would've fought over Hermia anyway, but now they fight over Helena, which inspires Hermia to try to fight Helena. During this row in the woods, some pretty harsh words are thrown around, and ugly things get brought up from the past (like how Helena thought Hermia was a vixen when they were younger). It's especially hard to hear the girls say things like this when you know they aren't under any kind of spell (only the guys are). Titania's love for Bottom is climactic insofar as it lets us know there will be a turning point. Eventually, Oberon will have Titania released from the spell (once he gets the Indian child) and likely he'll have everything fixed with the lovers by then, too. Until then, we can enjoy the madness at the peak of the play.
Suspense
Puck leads Demetrius and Lysander in opposite directions; Hermia and Helena's fight seems irreparable.
This part of the play would be a bit worrisome if we didn't know already that comedies end nicely. Demetrius and Lysander haven't resolved their quarrel and, even as they fall asleep, they're vowing to kill each other. Even more frightening is the emotional quarrel that's occurred between two formerly dear friends, Hermia and Helena. Helena runs away from a fuming Hermia, and the Jerry Springer-esquethings they said to each other leave open the distinct possibility that, no matter what, their friendship might never recover.
Denouement
Oberon releases Titania from the spell. Puck gives Lysander the remedy juice. Demetrius declares that he's in love with Helena. Theseus announces that the couples will be married. And Bottom awakens with his own head back.
Oberon has gotten the Indian child that he wanted from Titania, so he no longer has any beef with his wife. When she wakes up from her enchantment, the couple goes back to normal, which restores harmony to the natural world. Puck solves the problem of Lysander loving Helena by putting the potion's remedy on Lysander's eyes. He solves the problem of Demetrius not loving Helena by leaving the pansy-juice on Demetrius's eyes. Thus, when everyone wakes up, the couples have neatly paired off. Finally, the transformation and return of a normal-headed Bottom to Athens solves the Mechanicals' worry that they couldn't put on the play.
Conclusion
The three couples are married in Athens. Pyramus and Thisbe is performed. Oberon, Titania, and Puck bless the house and the couples.
All the Mechanicals' hard work finally pays off—they get to perform a play that touches on the severity of what could have happened to two doomed lovers (Pyramus and Thisbe here serve as a tragic reflection of the happier Lysander and Hermia). While the humans leave the play in party hats, the fairies come out and close the play, saying matters in the world are really more serious than all this might suggest. Puck reminds us that everyone will die, which is a nice conclusion. Oberon and Titania offer the real conclusion by promising that the characters are all busy (even while they speak) making babies, which is a good way to preserve yourself from death. Also, Oberon promises the couples will be happy and in love for the rest of their lives.