A metaphor is a type of figurative analogy. Analogies compare two things to show their similarities. Metaphors are very specific analogies in that they don't merely say that something is like something else in the way that similes do; instead, metaphors say that something is something else in a figurative sense, meaning not literally. Dr. Wheeler gives us Martin Luther's example of a metaphor, "A mighty fortress is our God" ("Literary Terms and Definitions: M"). In this line, the metaphor is comparing God to a fortress by saying that God is a fortress. However, of course, God is not literally a fortress; therefore, this is a figurative analogy. Many different metaphors can be found all throughout Shakespeare's plays, especially Romeo and Juliet. Below is an idea to help get you started.
One very interesting metaphor can be found in Prince Escalus's speech in the very first scene:
... you beasts,
That quench the fire of your pernicious rage
With purple fountains issuing from your veins! (I.i.79-81)
Even though the phrase "purple fountains issuing from your veins" does not contain the verb is, we know it is a metaphor because veins don't literally emit purple fountains. Instead, Shakespeare is using this metaphor to describe the vicious blood letting being caused by the feud between the Montagues and Capulets. What Shakespeare is comparing here is the blood that can spill from a flesh wound caused by a sword to a fountain pouring fourth purple liquid. Since a fountain pours forth much more fluid and much faster than just a vein, the metaphoric image is showing just how much blood the Montagues and Capulets are spilling.
Romeo compares his lips to "Two blushing pilgrims".
Romeo compares Juliet to the sun, "Arise fair sun and kill the envious moon".