A figure of speech is the use of language in a non-literal way, and the most common figures of speech are similes and metaphors. Also common are personification, metonymy, imagery, symbolism, and allusion. There are many other figures, but these are some of the most widely recognizable ones. Here are a few examples of figurative language found in the play, Hamlet.
Simile: a stated comparison using like or as.
In his first soliloquy in Act 1, Hamlet expresses his dismay at how his mother could go from being married to man as great as King Hamlet to being married to man who is so much less than that. He makes a rather complicated comparison to express the extreme difference between the two men. He says, "My father's brother, but no more like my father / Than I to Hercules." He is saying that Claudius is no more like King Hamlet than Hamlet is like Hercules.
Metaphor: an implied comparison between unalike things.
When Hamlet is expressing his disgust with his mother's marriage to Claudius, he compares this corruption of the state of Denmark to a garden. He says, "'Tis an unweeded garden that grows to seed; things rank and gross in nature possess it merely."
Personification: assigning human qualities or abilities to a non-human thing.
Horatio describes the dawn with the words, "the morn, in russet mantle clad, / Walks o'er the dew of you high eastern hill." Clearly, the rising sun and the morning cannot wear a coat or actually, walk -- but the line describes the color and the movement of the sun at early dawn.
Symbolism: using a actual thing to represent an idea
In Ophelia's display of crazy behavior in Act 4 she hands out various flowers to Claudius, Gertrude and her brother. In her speech to tells each receiver what each flower symbolizes. For examples she gives Laertes pansies and says "that for thoughts." Pansies were used a symbol of remembrance in the time of Shakespeare. She hands Claudius the flower rue and tells him it is called "herb of grace o' Sundays." Rue was a flower associated with repentance that could achieved through Grace with reconcillation.
Metonymy: using something associated with the thing to represent the whole of the thing.
In Act 3, after the "get thee to a nunnery scene," Ophelia comments and Hamlet changed behavior and thinks he has truly lost his mind. She states "O, what a noble mind is here o'erthrown! / The courtier's, soldier's, scholar's eye, tongue, sword ... [is] quite down." She names three aspects of Hamlet's character and then references three things associated with those descriptions -- Hamlet is a soldier (reference to the sword); Hamlet is a courtier (reference to the tongue); Hamlet is a scholar (reference to the eye).
Also -- all references to the throne are not referring the chair, but the King of Denmark who is associated with the throne.
Imagery: language used to appeal to any of the senses
There are examples all throughout the text where Shakespeare uses descriptive language to clarify the scene. One example is when Marcellus states that the arrival of the ghost suggests that something is "rotten in the state of Denmark." This could be a image to draw on the sense of sight and smell.
Allusion: a reference to something historical or literary
In Act 1, Horatio is comparing the arrival of the ghost to some of the omens that occurred before the assassination of Julius Caesar "in the palmy state of Rome."