Her first appearance is in the fifth book of the series, Harry Potter and the Order of the Phoenix. We first meet her as one of Harry's interrogators as he is tried on charges of unauthorised practice of underage sorcery before the Wizengamot, a wizard's court. She is Senior Undersecretary to the Minister of Magic, and is described as looking like a large pale toad, wearing a little black velvet bow in her hair that reminds Harry of a fly about to be caught.
(The name Dolores has the word dolor, or pain, as its root, and the name Umbridge is pronounced the same as umbrage, meaning resentment or pique at an often imagined insult. This sort of self-referential naming is common in the Harry Potter series; see Remus Lupin, Severus Snape, and Gilderoy Lockhart for more examples.)
Dolores Umbridge sets the action of the book into motion by taking umbrage at the suggestion made by Albus Dumbledore at the trial that the Dementors who attacked Harry were under Ministry of Magic control. Later in the book, it is revealed that Umbridge herself ordered the Dementors to attack Harry, a classic example of misdirection.
She is installed at Hogwarts as the new Defence Against the Dark Arts professor by order of the Ministry of Magic, teaching according to a politically restricted curriculum which would result in the students learning strictly the theory of Defence Against the Dark Arts; without the teaching of practical applications, most of the students feel that they will be left defenceless against the Dark Arts. When Harry contradicts the Ministry of Magic's official position that Lord Voldemort is dead, Umbridge is again offended, and punishes him by forcing him to write "I must not tell lies" over and over again in his own blood.
Her power increases as she is appointed the first ever "Hogwarts High Inquisitor", in which position she proceeds to evaluate the teachers at Hogwarts. When Harry forms a group to teach practical Defence Against the Dark Arts, Umbridge abolishes all student groups of three or more members; when Harry gives an interview about Lord Voldemort to The Quibbler, Umbridge bans possession of the magazine. These actions are sanctioned by the Ministry of Magic in the form of Decrees. With her new power, she fires Sybill Trelawney, professor of Divination, and is offended when Dumbledore replaces her with a centaur, since as a mixture of human and horse he is not of "pure blood", but a "filthy half-breed".
With the formation of an Inquisitorial Squad, which rewards some students for reporting on others and sanctions them to act as enforcement goon squads, it becomes clear that the character of Dolores Umbridge draws upon the history of fascism for inspiration. She tries to prosecute Harry for forming the Defence of Dark Arts club, but Dumbledore takes the blame, and leaves Hogwarts. Umbridge replaces him as Headmasteriss. She fires Hagrid, another mixed-race teacher as well. When firing Hagrid, four wizards Umbridge brought along seriously injures Professor Minerva McGonagall, when protest was made about the force used to handle Hagrid.
She also interferes with Harry's attempt to contact his godfather Sirius Black, but is outwitted by Hermione Granger, who tricks her into going into the Forbidden Forest, where she is subdued and almost killed by a herd of centaurs. (She is ultimately rescued by Dumbledore. How Dumbledore manages to rescue her from the human-hating centaurs without suffering any injury himself remains a mystery.)
After Voldemort appears in the Ministry of Magic - and is seen by a number of people, including Cornelius Fudge, the Minister of Magic himself, proving that Dumbledore has been right about Voldemort having returned. Dumbledore is restored as the Headmaster and Umbridge, who had been in the school infirmary, attempts to leave the castle without anyone noticing (Presumably she is ashamed). Peeves the Poltergeist discoveres her and chases her out with a walking stick and a sock full of chalk. As McGonagall notes, she expressed regret at not being able to chase Umbridge herself, because Peeves had borrowed her walking stick.