Kip Wheeler of Carson-Newman College defines style as:
The author's words and the characteristic way that writer uses language to achieve certain effects. ... the way the author uses words. ... word choice and sentence structure ... imagery, figurative devices, repetition, or allusion ....
Some of the elements of style that Shakespeare uses often are conflict, verbal asides and soliloquies (and the strong characterizations that accompany them), and his poetry.
In Shakepeare's play, Hamlet, conflict plays an enormous part in the plot's development. Hamlet is conflicted on almost every front. He trusts Horatio, but all others fall under suspicion.
Hamlet cannot feel safe speaking to those around him: his mother Gertrude has married the man who murdered his father, and Ophelia must be a dutiful subject to the King, and daughter to Polonius, sharing what she learns from Hamlet. Even Old Hamlet is an unknown: is he an "honest" ghost or one sent by the powers of darkness to trick Hamlet into relinquishing his eternal soul in trying to avenge his father's murder?
HAMLET:Angels and ministers of grace defend us!
Be thou a spirit of health or goblin damn'd,
Bring with thee airs from heaven or blasts from hell,
Be thy intents wicked or charitable, (45)
Thou comest in such a questionable shape
That I will speak to thee. (I, iv, 42-47)
Shakespeare uses conflict to move the plot, as well as provide insight into Hamlet's mind; Hamlet is continually torn between doing what is right for his father's sake, as well as trying not to lose his soul.
Another element of style that Shakespeare employs often are soliloquies.
In Hamlet's famous soliloquy (in Act Three, scene one), Shakespeare allows our protagonist, who can trust almost no one, to share his thoughts aloud so we may know what troubles him. Here, he toys with suicide, which is an immortal sin, and a frightening step into the unknown.
To be, or not to be, that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune
Or to take arms against a sea of troubles,
And by opposing end them...
There are several soliloquies in the play that open Hamlet's mind to us as he struggles with indecision. Shakespeare makes Hamlet more human and believable, beleaguered by doubts every step of the way. These speeches also highlight some of Shakespeare's finest (and most famous) writing.
In terms of the aside, it can often be shorter, acting as a side comment (that only that audience can hear), which can be delivered by any character, providing the audience with more telling information into that person's character and plans.
But now, my cousin Hamlet, and my son—
A little more than kin, and less than kind. (I, ii, 64-65]
The play on words here indicate that although Claudius refers to Hamlet as his "son," Hamlet delivers a silent rebuff, intimating that although they may be related ("kin"), they are nothing alike (similar to "of a kind"), and that Claudius is not nice ("kind"). These kinds of comments are much like verbal swordplay, and Hamlet gets away with them, and confuses his fellow characters in the play, by pretending to be insane.
Lastly, a perfect example of the Bard's poetry is found here:
Doubt thou the stars are fire,
Doubt that the sun doth move,
Doubt truth to be a liar,
But never doubt I love. (II, ii, 121-124)
Though Shakespeare uses may elements of style, these are a few I find that I enjoy the most.