In Act I, Scene II, Hamlet is bemoaning the fact that shortly after the death of his father, his mother married his uncle. He begins with the famous line:
"O, that this too too sullied flesh would melt,
Thaw and resolve itself into a dew...( I,ii,131-133)
If you read this carefully, you can see that Hamlet is using a play on words in the second line with the words "a dew". In French, this could be written "adieu", meaning good-bye. In other words, Hamlet that his flesh would bid "adieu" and die. He reinforces this idea in the next line with,
"Or that the Everlasting had not fix'd
His canon 'gainst self-slaughter! O God! God!" ( I,ii,134-135)
In other words, he wishes suicide was not a sin.
After remarking how awful the world seems to him, in line 140, he begins to complain about his mother's marriage to a "satyr" or a sex-crazed goat. He remembers how she used to "hang on" his father and then is furious with her for marrying his uncle "within a month" of his father's death. He then announces the famous line, "Frailty, thy name is woman" and criticizes his mother for her short time in mourning. He claims she only married "to post with such dexterity to incestuous sheet", thus accusing Gertrude of incest. He forecasts the marriage "cannot come to good" but wisely tells himself to "hold [his] tongue." Immediately following his complaint, he learns about the ghost of his father and the plot immediately thickens.
His first soliloquy is found in Act 1 scene 2 after his mother and Claudius lecture him about having a more "chin-up" attitude about his father's death. After they leave the stage, Hamlet moans and groans about how awful life is, and how he wishes he could just "melt, thaw and resolve...into a dew" or that he could just take his own life away (he says he can't because God has forbidden "self-slaughter"). He feels the world is "weary, stale, flat and unprofitable" and that only things "rank and gross" possess it. And, then he seems to indicate that the rank and gross things that possess the world are his mother's seeming fickle love for his father. He can't believe that his mom, who"would hang on" his father, "within a month...married my uncle" before even "the salt of most unrighteous tears had left the flushing in her galled eyes".
In this soliloquy, Hamlet is miserable, and finds the world miserable because of his mother's quick mourning of his father, and quick switch of affections to his uncle. He finds it gross, frail, incestuous, wicked, and feels that "it connot come to good."