Well, it relies on a magic potion, probably of the Friar's own making. Here's what he says:
Go home, be merry, give consent
To marry Paris. Wednesday is to-morrow.
To-morrow night look that thou lie alone;
Let not the nurse lie with thee in thy chamber.
Take thou this vial, being then in bed,
And this distilled liquor drink thou off
Each part, depriv'd of supple government,
Shall, stiff and stark and cold, appear like death...
Juliet has to go home and agree to marry Paris. Then, the night before the wedding, she'll sleep by herself in her bedroom, and take the vial (bottle) of potion that Friar Laurence is giving her. This will make her seem like she is dead.
And in this borrowed likeness of shrunk death
Thou shalt continue two-and-forty hours,
And then awake as from a pleasant sleep.
Now, when the bridegroom in the morning comes
To rouse thee from thy bed, there art thou dead.
Then, as the manner of our country is,
In thy best robes uncovered on the bier
Thou shalt be borne to that same ancient vault
Where all the kindred of the Capulets lie.
The next morning, Paris will come to get her out of her bed, and she will be dead. They'll leave her on a funeral bier, cltohed, and take her to the Capulet vault.
In the mean time, against thou shalt awake,
Shall Romeo by my letters know our drift;
And hither shall he come; and he and I
Will watch thy waking, and that very night
Shall Romeo bear thee hence to Mantua.
In the meantime, before she wakes up, Friar Laurence will write to Romeo and explain everything him. Then, Friar Laurence and Romeo will watch Juliet wake up in the vault - and then Romeo will take her away to Mantua.