"Give her of the fruit of her hands." We all eat the fruit of whatever seeds we sow in our lives. This woman's "fruits" are good and desirable, because she leads a pure, sound and godly life. The writer's prophecy says to give her of this fruit, like a prize, for she has earned and is deserving of it. God gives unto us in just that way -- her fruits of goodness, of charity, and of righteous living are released back unto her in abundance, for her good pleasure -- for such is what she has sown. The laws of sowing and reaping are very powerful, as are all God's laws, and the Proverbs 31 woman can always enjoy her harvest.
The second phrase of this verse reads, "and let her own works praise her." Again, her own works -- her deeds -- all have a consistently advantageous outcome, such that the works themselves come back in praise to her as opposed to "coming back to haunt her," as the saying goes. Her works bring her praise and honor from others, as well. Some of her activities may have an ever-present, long-term benefit to the community. Their existence therefore continually brings thanks and commendation back to her. She is always there to lend a hand to others, to help those in need, to act justly and fairly, and such never goes unnoticed. Important, however, is her motivation, which stems from a generous heart and not for want of glory from men.
Part of her "works," in this sense, might also include how well she has raised her children. As they grow up in the community and as they lead their lives as adults, they continually bring praise to her in their righteous ways and, in following her example, in the benefit and service they bring to others.
Her works praise her "in the gates of the city." In biblical times, the elders and judges of a town or city congregated at the city gates, to hear cases and discuss important issues that affected the city and its townspeople. Here, the writer is telling us that she and her works are noted by important, publicly known people of the city in which she lives. It follows that these works must be noteworthy and consistent to bring her such honor. She is held in high regard and esteem by moral, wise people. Plus, if those in high stead are aware of her works, local townspeople must be as well, who also give her praise and admiration.
Another biblical example of this can be found in Acts 9:36-39, the death of a woman named Dorcas. Like the Proverbs 31 woman, she is known and remembered for her good works and righteous way of life.