decided to give Romeo her answer later.  She sent Nurse as a messenger.

Romeo waits for Nurse to come.  After some good-natured rubbing with his friends, he receives Juliet’s answer from her about agreeing to marry him.  Romeo tells Nurse that Juliet should meet him at Friar Lawrence’s cell, where they will secretly marry.

Bid her devise some means to come to shrift

This afternoon;

And there she shall at Friar Laurence’ cell

Be shriv'd and married. Here is for thy pains. (Act 2, Scene 4)

Nurse is Juliet’s confidant.  She has raised her from a baby.  She had a daughter Juliet’s age who died, and therefore loves Juliet like her own.  She cares for Juliet.  While she laughs and teases both of them, especially about Romeo having no manners

He is not the flower of courtesy, but, I'll warrant him, as gentle as a lamb. (Act 2, Scene 5)

She also feels that they are in love.  Even though she knows that it is forbidden she doesn’t care about that or the fact that they just met.  She is more than happy to act as go-between.

Romeo and Juliet do not go off and run away on their own.  They have a real wedding.  They are married by Friar Lawrence, who also disobeys their parents’ wishes and marries them.  He has an ulterior motive.  He hopes that by marrying them, he can put an end to the bloody feud.  Ultimately it does, but not before both young lovers lose their lives.

I believe that the Scene 4 in question is coming from Act 2. When this scene begins, Mercutio and Benvolio are talking. Romeo and Tybalt are both topics of conversation, and eventually Romeo enters the scene. Then the scene gets raunchy as the three teens tell some really dirty jokes. The nurse shows up, and amazingly the jokes get even dirtier. She is eventually able to speak with just Romeo. The nurse explains that she has sought Romeo out on Juliet's behalf, and the nurse is quite frank with Romeo. She warns him that he better not be misleading Juliet's feelings.

but first let me tell ye, if ye should lead her into
a fool's paradise, as they say, it were a very gross
kind of behavior, as they say: for the gentlewoman
is young;

Romeo assures the nurse that he is definitely in love with the girl that he met less than 24 hours earlier. Then he shares his "plan" with the nurse. I hesitate to call it Romeo's plan. He does plan to marry Juliet, but he tells the nurse to tell Juliet to come up with a plan to get out of the house and meet him. He doesn't actually offer any solutions for how Juliet might accomplish this task.

Bid her devise
Some means to come to shrift this afternoon;
And there she shall at Friar Laurence' cell
Be shrived and married. Here is for thy pains.

Just before the nurse leaves, Romeo says that he'll make sure the nurse gets a rope ladder. Apparently it's up to the nurse to figure out how to hang the ladder so that it supports Romeo's weight and isn't visible by anybody else.

And stay, good nurse, behind the abbey wall:
Within this hour my man shall be with thee
And bring thee cords made like a tackled stair;
Which to the high top-gallant of my joy
Must be my convoy in the secret night.