The Friar is both a holy man and a naturalist. He is an expert in plants and natural remedies. At first, he is a trusted advisor to young Romeo, a confidante. By the play's end, he has become a mad scientist, like Victor Frankenstein, who tries to conquer death, all in the name of love. His mistakes, like Victor's, relate to his isolation, his lack of community, his going "rogue."
As a rogue friar, he tries to cross-breed two unlike flowers (Romeo and Juliet) in an effort to produce a natural, sweeter hybrid. He wants to breed out the hate, or at least to extract it for medicinal use. Observe his soliloquy:
He thinks that by secretly marrying Romeo and Juliet he can use "hate" as medicinal power. As he sees it a chain of events will thus occur making the the two families reconcile since marriage and love are natural antidotes to hate. He figures that "what God has joined together, let no man put asunder." As a believer in the Great Chain of Being, he thinks that the married couple's love is now above their parents' hate, as it is ordained by God.
His plan is broad, and he forgets to come up with contingencies to account for minor problems. Such was the idealistic thinking of religious thought: its focus is too much on heaven, not enough on earth.
This happens in Act III, Scene 3 and Act IV, Scene 1. You can read it yourself and get a more complete idea of the plan than I can provide here.
But the basic idea is that Romeo will leave the city and go to Mantua. Meanwhile, the Friar will talk to the families.
But then Lord Capulet starts insisting that Juliet must marry Paris. So then Friar Laurence comes up with his second plan. Juliet will drink the potion. Her family will think she's dead and they'll place her in the family tomb. By the time Romeo gets back from Mantua, she'll have awakened and the two of them can leave together.