What are different ways in which Shakespeare tries to please his audiences,both the aristocrats and commoners in A Midsummer Night's...

Shakespeare wrote his plays with both the upper classes and the lower--the "groundlings"--in mind.  In his play A Midsummer Night's Dream, both audiences would certainly enjoy the antics of Puck and the other fairies.  Of course, the poetic language and the higher thought of the play appealed more to the upper classes who were educated.

One example that serves to explain how Shakespeare appealed to both audiences occurs in the second act after Oberon has set in motion his plan for revenge on his wife, Titiana, Puck mismanages his instructions and "alienates" the wrong choice of husband for Hermia, so that he, Lysander, is now in love with Helena. Lysander tells Helena,

Not Hermia but Helena I love:/Who will not change a raven for a dove?/The will of man is by reason sway'd/And reason says you are the worthier maid./Things growing are not ripe until their season:/So I, being young, till now ripe not to reason;/And touching now the point of human skill,/Reason becomes the marshal to my will,/And leads me to your eyes; where I o'erlook/Love's stories, written in lover's richest book. (II,ii,114-124)

In this passage, the groundlings would enjoy the misadventures of Puck and the resulting action, as would the aristocrats.  In additon, though, the upper classes would enjoy the beauty of the metaphors and rhythm and rhyme of the passage as well as the irony of the observation of Lysander that "Reason becomes the marshal to my will."  The eye imagery, also, would not go unnoticed by the more educated audience.

In other words, the groundlings enjoyed the action of the play, the humorous situations such as the play that the --put on, and, of course, the hilarity of Bottom's having the head of an "ass," as well as some of the poetry of the play and the themes, but the upper classes would delight much more in the subtleties of the language and the immense expansion of Shakespeare's poetic imagination, as well as the motifs, such as the preoccupation with the significance of dreams and reality, that Shakespeare used.

Modern audiences of all kinds and ages are yet able to enjoy this delightful play.  (In one performance that was given Puck ran through the audience, sitting beside children to their delight.)  The physical actions of this play is most enjoyable to them as they see Bottom and the fairies and observe the chasing of Helen after Demetrius.  Adult audiences, who enjoy the humor of the play as well, also understand the sexual implications of this play and the beauty of the language; thus, they delight in it, as well.