How does Romeo change from Act I to Act II?

Romeo changes from being depressed over his unrequited love for Rosaline in Act I to being happily married to the girl of his dreams in Act II. When we first meet Romeo in Act I he is lovelorn. The woman he loves does not share his affection and is committed to avoiding love and remaining "chaste." Romeo says,

Well in that hit you miss. She’ll not be hitWith Cupid’s arrow. She hath Dian’s wit,...

Romeo changes from being depressed over his unrequited love for Rosaline in Act I to being happily married to the girl of his dreams in Act II. When we first meet Romeo in Act I he is lovelorn. The woman he loves does not share his affection and is committed to avoiding love and remaining "chaste." Romeo says,

Well in that hit you miss. She’ll not be hit
With Cupid’s arrow. She hath Dian’s wit,
And, in strong proof of chastity well armed,
From love’s weak childish bow she lives uncharmed.
She will not stay the siege of loving terms,
Nor bide th’ encounter of assailing eyes,
Nor ope her lap to saint-seducing gold.
O, she is rich in beauty, only poor
That, when she dies, with beauty dies her store.

Romeo's cousin Benvolio tries to convince Romeo that Rosaline is not the only woman in Verona and he needs to "examine other beauties." When a servant asks Romeo to read the invitations to Capulet's party Romeo discovers Rosaline will be there, and Benvolio thinks it will be good for Romeo to see her in company with others. He says,

At this same ancient feast of Capulet’s
Sups the fair Rosaline whom thou so loves,
With all the admirèd beauties of Verona.
Go thither, and with unattainted eye
Compare her face with some that I shall show,
And I will make thee think thy swan a crow.

Benvolio, of course, is right. Once Romeo sees Juliet he totally forgets Rosaline. Even the feud between the families cannot dissuade Romeo from pursuing Juliet and within about an hour of first meeting the girl he proposes marriage. He convinces Friar Lawrence to perform the ceremony (the Friar believes the union will end the feud). Thus, Romeo goes from totally dispirited to being happy and fulfilled by his love for Juliet. 

In many ways, however, Romeo has not changed. He remains impetuous and often doesn't think through his actions. He ignores the Friar's advice about taking things slowly. The Friar says, 

These violent delights have violent ends
And in their triumph die, like fire and powder,
Which, as they kiss, consume. The sweetest honey
Is loathsome in his own deliciousness
And in the taste confounds the appetite.
Therefore love moderately. Long love doth so.
Too swift arrives as tardy as too slow.

The Friar is prophetic. Romeo does not "love moderately." He rushes head long into the events which ultimately propel the two young lovers to their eventual double suicide.