An allusion is a moment when an author makes a reference to another work of literature. The reference can include "a person, place, event, or another passage" found in another piece of literature (Dr. Wheeler, "Literary Terms and Definitions"). Romeo and Juliet is most definitely full of allusions. Several different allusions can actually be found in the very fist scene. Most of Shakespeare's allusions refer to either Greek or Roman mythology, and these serve as allusions because Greek and Roman mythology was recorded in writing. Therefore, any reference to Greek or Roman mythology is a literary reference. Below are a few allusions explained to help you get started.
After Prince Escalus breaks up the whole-city riot, we see Lord Montague talking with Benvolio about how he is concerned about his son Romeo. One thing Montague says is that Romeo has been seen at dawn crying morning after morning. He also says that at dawn, Romeo finally retires to his room to sleep, drawing the curtains. Montague describes the dawn in the lines:
... But all so soon as the all-cheering sun
Should in the farthest East begin to draw
The shady curtains from Aurora's bed... (I.i.130-32)
The phrase "draw the shady curtains from Aurora's bed" refers to Roman mythology and is therefore an example of allusion. Aurora was the Roman goddess of the dawn. The image portrays the sun drawing the curtains from the goddess of the dawn's bed.
Romeo later makes two more allusions to Roman mythology. Romeo refers to Cupid in the lines, "Alas that love, whose view is muffled still, / Should without eyes see pathways to his will!" (169-70). Cupid is the Roman god of erotic love and is always portrayed as being blind folded. Hence, we know that this reference to love with a "muffled" view, or blind view, is actually an allusion to Cupid. Later, when talking about Rosaline, he says:
She hath Dian's wit,
And, in strong proof of chastity well arm'd,
From Love's weak childish bow she lives uharm'd. (211-13)
Diana was the goddess of both hunting and childbirth. However, ironically, as the goddess of childbirth, she was also a sworn virgin. Hence, Romeo is saying here that, like Diana, Rosaline has vowed to remain chaste. Therefore, we see that this reference to "Dian" and "Chastity" is an allusion to the goddess Diana of Roman mythology.