How did Romeo and Juliet communicate with each other in Romeo and Juliet? Please provide quotes and citations.

Romeo and Juliet communicate primarily through Juliet's nurse when they are apart.  On the night when they first meet, after Romeo has scaled the walls into the garden beneath Juliet's balcony, they speak for a while, and Juliet eventually says that she will send someone to Romeo the next day, someone who will deliver a message to her: "If that thy bent of love be honorable, / Thy purpose marriage, send me word tomorrow, /...

Romeo and Juliet communicate primarily through Juliet's nurse when they are apart.  On the night when they first meet, after Romeo has scaled the walls into the garden beneath Juliet's balcony, they speak for a while, and Juliet eventually says that she will send someone to Romeo the next day, someone who will deliver a message to her: "If that thy bent of love be honorable, / Thy purpose marriage, send me word tomorrow, / By one that I'll procure to come to thee [...]" (2.2.150-152).  In other words, if Romeo wants to marry her, he should send a message about when and where the ceremony will be performed. 

Sure enough, the next day, after Romeo has spoken with Friar Lawrence, the nurse finds Romeo.  He advises her to tell Juliet to come up with some reason that she needs to go to confession that afternoon, and he will be waiting there to marry her (2.4.183-186). 

Later, when Romeo is hiding at the friar's cell after having killed Tybalt, Juliet sends her nurse to him again.  Speaking to Romeo, the nurse says, "My lord, I'll tell my lady you will come [....].  Here, sir, a ring she bid me give you, sir" (3.3.171-173).  Therefore, the nurse is really the main mode of communication by which the young lovers communicate.