Ancient_Geezer has a great table that shows how it works and he is much better at answering to the specifics that me, but I'll give it a shot.
Basically, the poverty levels dictate the amount of tax-exempt spending by an individual or family. Depending on the size of the family, the amount of spending that is tax-exempt will fluctuate. Assuming the poverty level is $20,000 for an individual, my first $4,600 in spending would be considered "tax-exempt" (20K*.23). Since it isn't possible (that I can figure) to track that spending by any specific individual, they would send me a monthly stipend of $383.333333.
A few of the FR opponents of the fair tax have brought up a valid concern for me. That is that this system would put all citizens on the government payroll, everyone would receive a monthly check. However, I see this one potential negative to be far outweighed by the positives of the entire paradigm shift.
Would the poverty level be jiggered by area of the country? Its more expensive to live in NYC or LA than in Dubuque.
I would like to see the bill have the "poverty level" tied to perhaps the bottom 10, 15, or 20% of income earned, without the possibility of adjustment from that percentage.