In "Romeo and Juliet," how does the concept of predetermined destiny relate to the two lovers and the play itself? Romeo and Juliet are referred to...

Being 'star-cross'd' plays out in the rash actions of all the characters.  Emotions control the reactions of the characters, which suggests that "fate" is pulling them along.  Juliet herself comments on this after the balcony scene:  "Although I joy in thee,
I have no joy of this contract tonight,
It is too rash, too unadvis'd, too sudden." 

It is the family hatred that causes Romeo and Juliet to feel that they must keep their love secret.  This leads to elopement and later to Juliet's faked death - she can not marry Paris, but she can not tell her parents why.  The emotional attack by Tybalt causes Mercutio's death, which leads to Tybalt's death, which leads to Romeo's banishment...  With the exception of the letter that just didn't arrive on time, the "fate" of the story is about the emotional behaviors of the characters.

Here is a quote from Juliet about fate (fortune):

O Fortune, Fortune, all men call thee fickle;
If thou art fickle, what dost thou with him
That is renown'd for faith?

Because of the difficulty in the relationship, Juliet feels at the mercy of fate.

The "forebodings" of the characters also reference fate.  Romeo has misgivings before the party:   "I fear, too early, for my mind misgives/Some consequence yet hanging in the stars/Shall bitterly begin his fearful date".   Juliet believes she sees Romeo as "one dead/at the bottom of a grave".