Romeo avoids his friends who know what Romeo is doing and, therefore, make jokes at his expense.  Romeo leaps over the Capulet's wall in order to be closer to Juliet saying, "Can I go forward when my heart is here?"  Meanwhile, Benvolio and Mercutio continue to look for Romeo, knowing full well that Romeo is lovesick.  Mercutio takes full advantage of this by making fun of Romeo.  "The ape is dead, and I must conjure him. / I conjure thee by Rosaline's bright eyes, / By her high forehead and her scarlet lip, . . and quivering thigh."  Mercutio here jokes that Romeo is "the ape" and that he can conjure him by using parts of Rosaline who, little does Mercutio know, has already been cast aside by Romeo in favor of Juliet.  When Mercutio takes his joke a bit too far, Benvolio admits, "And if he hear thee, thou wilt anger him."  Considering Romeo only seems to think of love, I doubt he would be angered.

The basis of the humour in this scene lies particularly in Mercutio's witticisms and the use of ambiguity and puns when he speaks to Romeo and later, to the nurse.

When Romeo arrives and apologises for misleading them by giving them the slip (slipping away from their company), Mercutio comments that:

That's as much as to say, such a case as yours
constrains a man to bow in the hams.

He makes fun of Romeo by suggesting that it is easy for Romeo to say but, sarcastically a (sad) situation such as Romeo's, forces a man to be overly courteous - so much so that he bows very deeply. In other words, an almost servile obedience. Romeo interprets this as giving a curtsy (play on courtesy).

Their continued talk is filled with further word-play and witticisms. Mercutio says that Romeo got it right (the definition of courteous) and Romeo retorts that Mercutio has given 'a most courteous exposition' - further wordplay. He means that Mercutio has most kindly explained the word - obviously there's a slight hint of sarcasm here as well.

Mercutio's reply that:

Nay, I am the very pink of courtesy.

Romeo understands 'pink' as meaning 'flower' - in other words, Mercutio is the epitome of courtesy. As a flower puts on a show with its petals and colours to impress, so does Mercutio with his 'courtesy'. when Mercutio agrees to this definition, Romeo jests further that his shoe in this regard is therefore 'well-flowered'. The audience would surely laugh at this remark since the foot would be used to kick an offender in the bottom or such sort.

Mercutio displays further wit saying that Romeo should extend the joke until it is worn out (has become stale) and only the bare foot is left. There would probably be more laughter since Mercutio is referring to both the literal and figurative.  

Romeo, however, seems to have grown tired of the joke already and wittily implies that the joke is for dumb people only.

O single-soled jest, solely singular for the
singleness.

He says that the joke is silly and only unique because it's the only joke that Mercutio knows. Mercutio feints being hurt by this remark and turns to Benvolio to intervene.

Come between us, good Benvolio; my wits faint.

he means that he is losing his sharpness (wits). Romeo, however, seems to now have warmed up to the challenge and wants to match his wit against Mercutio's. Mercutio, however does not want to enter into a 'wild goose chase' with Romeo and acknowledges that Romeo has more wild goose in one of his wits than he has in his whole five (a reference to the five senses).

The humorous play continues with the word 'goose' now being the pun. Mercutio asks Romeo if he identifies with the word goose - obviously a derogatory term, but Romeo declares that whenever Mercutio had been with him, he (Mercutio) was the goose. Mercutio says that he would bite Romeo's ear for that remark - indicating his pleasure. He further says that Romeo's wit is biting, on which Romeo replies that it is the perfect sauce to be served with goose. This would obviously make the audience laugh as well, since Mercutio, metaphorically is the goose.

The two continue their verbal duel until they are interrupted by the arrival of the nurse and Peter. This event also leads to a number of rich and bawdy witticisms being offered by all three, somewhat to the chagrin of the poor nurse who has only come to do her duty and convey an important message to Romeo. 

This whole repartee concludes

Shakespeare's Romeo and Juliet is a tragedy, but it does have episodes of humor, particularly in the first two Acts. In fact, if the play had ended after Act II, Scene 6 it would be labeled as a comedy with the marriage of Romeo and Juliet. Shakespeare's comedies usually end in a wedding and his tragedies end in death. Comedy is in evidence throughout those first two Acts.

In Act I, Scene 2, the servingman serves a comedic role when he is not able to read the list of people he is supposed to invite to Capulet's party. In fact, the servingmen in the beginning of Act I, Scene 5 are added to bring a humorous touch to the play. Picture the Three Stooges with lots of slapstick.

The biggest laughs probably come in Act I, Scene 3 when the Nurse is talking about Juliet's age. She recalls a bawdy story about her late husband who commented on Juliet falling on her face when she was only a toddler. He suggests the girl will want to fall on her back when she is older. The Nurse says,

For then she could stand high-lone. Nay, by th’
rood,
She could have run and waddled all about,
For even the day before, she broke her brow,
And then my husband (God be with his soul,
He was a merry man) took up the child.
“Yea,” quoth he, “Dost thou fall upon thy face?
Thou wilt fall backward when thou hast more wit,
Wilt thou not, Jule?” And, by my holidam,
The pretty wretch left crying and said “Ay.”
To see now how a jest shall come about!
I warrant, an I should live a thousand years,
I never should forget it. “Wilt thou not, Jule?”
quoth he.

Nurse: My fan, Peter.

Mercutio: Good, Peter, to hide her face, for her fan’s the fairer face.

Nurse: God ye good morrow, gentlemen.

Mercutio: God ye good e'en, fair gentlewoman.

Nurse: Is it good e'en?

Mercutio: 'Tis no less, I tell you, for the bawdy hand of the dial is now upon the prick of noon. 

No, ’tis not so deep as a well, nor so wide as
a church door, but ’tis enough. ’Twill serve. Ask for
me tomorrow, and you shall find me a grave man.