When Romeo sneaks into Juliet's garden, the two converse and share lovers' vows. Near the end of their conversation, Juliet says to Romeo,
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,
Where and what time thou wilt perform the rite (2.2.150-153).
In other words, Juliet plans to send her Nurse to visit Romeo to learn if he wants to marry her and when and where the ceremony will take place. Romeo then goes to visit Friar Lawrence, both to acquaint him with the news of Romeo's love for Juliet as well as to ask the friar to perform the wedding. Friar Lawrence agrees to marry the young couple because he hopes that
this alliance may so happy prove
To turn your households' rancor to pure love (2.3.98-99).
He wants to believe that the marriage between Romeo and Juliet will end the bloody feud between their families. Later, the Nurse visits Romeo, and Romeo tells her,
Bid [Juliet] devise
Some means to come to shrift this afternoon,
And there she shall at Friar Lawrence' cell
Be shrived and married (2.4.183-186).
He wants Juliet to tell her parents that she's going to confession, which would explain why she's going to Friar Lawrence's cell, and that's when they'll get married. We do not actually get to witness the wedding of Romeo and Juliet, but it would occur immediately following act 2, scene 6. At the end of the scene, the friar and Romeo and Juliet are just about to begin the ceremony.