Hester is guilty of the "sin" of adultery. As punishment, is forced to stand on a platform in the town square, an example and a spectacle, for all to see. Thereafter, she is forced to affix a bright, red letter "A" which identifies her at all times to the community, to strangers, and to herself. The "A" brands her and never lets anyone forget her sin against both man and God.
The sentence, and the reaction by the majority of the community, is expressed Chapter Two, "The Recognition." A townsman delivers the news. Though some argue Hester should have been executed, the elders,
"...in their great mercy and tenderness of heart, they have doomed Mistress Prynne to stand only a space of three hours on the platform of the pillory, and then and thereafter, for the remainder of her natural life, to wear a mask of shame on her bosom."
"A wise sentence!" remarked a stranger, gravely bowing his head. "Thus she will be a living sermon against sin, until the ignominious letter be engraved on her tombstone."
Although Hester certainly did not commit her "crime" alone, her partner has escaped similar humiliation and punishment, a fact not lost on the stranger. He says,
"It irks me, nevertheless, that the partner of her iniquity should not, at least, stand on the scaffold by her side. But he will be known! -- he will be known! -- he will be known!"
A married woman who has obviously had relations with another man-she is pregnant and her husband is missing-Hester is an adultress. Her initial punishment is to stand before the townspeople on a scaffold and be interrogated publicly. Proudly she refuses to name her lover. Made to wear a letter identifying her as an adultress, she defiantly embroiders it with gold thread and artistry.
Ironically, it seems that Hester's pride (the rose outside the prison door) is the greatest of her sins, the one for which she will pay dearly as the comments of the sanctimonious bystanders about her vanity suggest: "she may cover it [the letter A with a brooch, or such like heathenish adornment..." The women are eager to see Hester branded or disfigured for her sin, an indication of their envy of her beauty and elegance. Her "reckless mood" also infuriates them.
For her refusal to humiliate herself, Hester is shunned, rebuffed by remarks and looks whenever she passes people. She lives alone with her daughter, Pearl, her beauty fades and her personality withers. It is only in the forest meeting with Dimmesdale when she removes her cap symbolically indicating a release, that her hair shines and her face resumes the bloom of youth.
In the end when the A no longer is a "mark of Cain," Hester still pays the price of her pride as she no longer has identity without the letter on her.
Can you give me examples from the text that says she has commited adultery? I am having trouble finding supporting text.