What's he saying?
"When in disgrace with fortune and men's eyes / I all alone beweep my outcast state,"
When I'm having bad luck and am looked down upon by other people, I cry alone in self-pity,
"And trouble deaf heaven with my bootless cries, / And look upon myself, and curse my fate,"
And pray, though it seems like no one hears my prayers, and feel sorry for myself,
"Wishing me like to one more rich in hope, / Featured like him, like him with friends possessed,"
Wishing I were more like someone with more hope in his life, or someone very handsome, or popular,
"Desiring this man's art, and that man's scope, / With what I most enjoy contented least;"
Wanting one person's talent, and another's opportunity, and things that usually make me happy only making me more upset;
"Yet in these thoughts my self almost despising, / Haply I think on thee, and then my state,"
Even though I am hating myself, I happen to think of you, and then,
"Like to the lark at break of day arising / From sullen earth, sings hymns at heaven's gate;"
Like a lark that sings at dawn, my situation seems to brighten and become hopeful;
"For thy sweet love remembered such wealth brings / That then I scorn to change my state with kings."
Because thinking of your love makes me feel so rich that I wouldn't switch places with kings.
Why is he saying it?
The emotional state of the speaker in Sonnet 29 is one of depression: in the first line, he assumes himself to be "in disgrace with fortune," meaning he has been having bad luck. He also feels in disgrace with "men's eyes," implying that the general public looks on him unfavorably. This could be real or imagined, but it is enforced in line 2, when he bemoans his "outcast state." Here, "state" refers to a state of being, and in this case, he is cast out from society.
Lines 3-4 make allusion to Job of the Old Testament in the Bible, who was cast out onto a dung heap and called to a God who didn't listen. The poet finds himself in the same situation: Heaven personified is God, and in this case he is "deaf," making the poet's cries "bootless," or useless. The idea of cursing one's fate also hearkens to Job, who cursed himself after falling out of God's favor.
The speaker finds himself envying what others have, and in lines 5-9 he sees almost everyone as having something he lacks. He wishes to be like "one more rich in hope," perhaps meaning hopeful or literally wealthy; "featured like him," refers to someone who is handsome, with beautiful features; and another is "with friends possessed," or popular, unlike the poet (as has been established in the first two lines). In line 7, he envies the artistic talent of one man, and the opportunities afforded someone else.
The simile of a lark is developed in lines 10-12, when the speaker describes the effect that a thought of his love has on his "state," or emotional well-being. The fact that the lark rises from the "sullen earth" at "break of day" implies that the day is much happier than the night; day break is compared to the dawning of a thought of the beloved. As the lark "sings hymns at heaven's gate," so the poet's soul is invigorated with the thought of the fair lord, and seems to sing to the sky with rejuvenated hope.
The final couplet of Sonnet 29 declares that this joyfulness brought about by a thought of the fair lord is enough to convince the speaker that he is better off than royalty. Here, "state" is a pun: it carries the meaning of emotional well-being, as it did earlier in the poem, and suggests that the love of the fair lord makes the speaker so happy that all the wealth of a king would not be better. But it also refers to a nation, or a kingdom.