In the first line of the this poem, Shakespeare uses synecdoche, a figure of speech in which a part represents the whole and vice versa. By stating that he is in disgrace with "men's eyes," he does not mean their eyes only, but their entire selves.
In line three, Shakespeare uses apostrophe by speaking of heaven as if it is a person who is deaf to his cries about his unfortunate situation. This can also be deemed personification since heaven is given a human persona, as if it can respond to his cries.
In lines five and six, Shakespeare uses similes, which are comparisons between two unlike things, usually using "like" or "as." In this instance, he is comparing himself to one who, he believes, is more fortunate than himself. He wishes to be as blessed as the other person and that he can have what he has, such as friends and good looks.
In line twelve, the speaker describes earth as being "sullen," which is also personification. He means that earth is in a depressed and sulky mood, which is a human characteristic. He is, in fact, describing his own depressed mood and contrasts it with his happy state by using a simile describing himself as a lark, a bird associated with joy and a sense of contentment.
The speaker uses the word "state" as a pun, which is a play on words. It has different connotations throughout the sonnet. In line two, it refers to his situation or condition, while in line 10 he is speaking about his mood. In the final line, "state" refers to his position, which he does not wish to substitute, even with that of kings, since he believes that he is truly fortunate to have in memory a friend who can bring him true love.
Assonance -- the repetition of vowel sounds is also used but is not that prominent. The poet uses assonance in line 3: "deaf heaven," which accentuates the fact that his cries go unheard.