The introduction, otherwise called the exposition, climax, and resolution of A Midsummer Night's Dream have already been addressed in a previous answer, but we can address rising action and falling action here. While there are subplots in A Midsummer Night's Dream, here we will be discussing the central plot of the lovers, that way you can apply to it the other subplots.
The events that fall under rising action are the events that that take place after the exposition and lead up to the climax. For the plot involving the Athenian lovers, the rising action begins when Lysander and Hermia make the decision to escape Athens via the woods in order to be married outside of Athens. Another moment of rising action occurs when Helena decides to betray to Demetrius Hermia and Lysander's secret plans with the chance that she might receive a simple "thank you" from Demetrius. Lysander and Hermia's decision, as well as Helena's decision, is the driving force that sends all four Athenian lovers into the woods, leading to the men's enchantment and the climax. We further see the rising action climb when Helena decides to follow after Demetrius into the woods while he is in pursuit of Hermia and Lysander. Seeing Demetrius being cruel to Helena in the woods leads Oberon to decide to use the "love-in-idleness flower" on Demetrius as well, which also leads to the climax.
The falling action is any action taking place after the climax that leads to the resolution of the play. For the lovers, the play is resolved once Theseus decrees that both couples should be married in the way that they are correctly paired. The climax occurs at the moment that Oberon and Puck witness just how much damage Puck's mix-up has caused, which can be observed through the four lovers' fight. The climax is also the moment when Oberon gives Puck commands to fix things again. In A Midsummer Night's Dream, the falling action for the plot concerning the lovers is actually very brief. The falling action takes place the moment when, per Oberon's instructions, Puck begins leading both Demetrius and Lysander all over the densely fogged woods until they are too exhausted to remain standing. Once they collapse, it is Oberon's plan to have Puck enchant Lysander with the flower once again so that when he awakes and sees Hermia, he will be back in love with her again, as we see in Oberon's lines:
Then crush this herb into Lysander's eye;
Whose liquor hath this virtuous property,
To take from thence all error with his might
And make his eyeballs roll with wonted sight. (III.ii.382-385)
The falling action continues once Puck induces Helena and Hermia to fall asleep as well next to the men, that way when they awake, they will be coupled appropriately.