Romeo's first reaction when Friar Lawrence tells him he is getting banished is basically to throw a tantrum. He moans and groans about how horrible a fate this is and he talks about killing himself. But then the Friar gets him to snap out of it.
Romeo's reaction changes because of the Friar's plan. The Friar says that he will try to get the two families to make up with each other. He will tell them that Romeo and Juliet have secretly gotten married. He hopes that the prince will forgive Romeo and Romeo will then be able to come home and be with Juliet.
When Romeo first learns of his banishment, he immediately jumps to conclusions and fails to see the opportunity within his sentence. As Romeo says:
There is no world without Verona walls,
But purgatory, torture, hell itself.
Hence-banished is banish'd from the world,
And world's exile is death: then banished,
Is death mis-term'd: calling death banishment,
Thou cutt'st my head off with a golden axe,
And smilest upon the stroke that murders me.
So soon forgotten was Friar Lawrence's advice just the day before to proceed "wisely and slow, they stumble that run fast."
After a fair amount of cajoling and lecturing, however; Friar Lawrence is able to help Romeo see the potential in his sentence:
Go, get thee to thy love, as was decreed,
Ascend her chamber, hence and comfort her:
But look thou stay not till the watch be set,
For then thou canst not pass to Mantua;
Where thou shalt live, till we can find a time
To blaze your marriage, reconcile your friends,
Beg pardon of the prince, and call thee back
With twenty hundred thousand times more joy
Than thou went'st forth in lamentation.
Finally, Romeo begins to calm down and in response to the Friar's plan and to a ring from Juliet, he says: