When we first meet Dolores Umbridge, she is sitting at the right hand of Fudge during Harry's hearing for use of magic as an underage wizard. As Senior Undersecretary to the Minister for Magic, she sneers openly at the idea that there could be dementors in a Muggle suburb. She is clearly a by-the-book Fudge supporter.
The plot thickens when Umbridge first arrives to become the latest in a string of Defense Against the Dark Arts teachers at Hogwarts. During the Welcome Feast, Professor Umbridge immediately launches into an incredibly boring speech that sends most of the students half to sleep. But Hermione is wide awake and listening, and she realizes that what Umbridge is saying is that the Ministry of Magic – headed by a man who fears Dumbledore and his power – is going to start interfering at Hogwarts. And interfere, Professor Umbridge does.
She refuses to allow any of her students to actually practice defensive magic. She claims that they should be learning theory only; practice suggests that they are going to need these defensive spells outside of the classroom, which is nonsense. When Harry leaps up and says that Voldemort is back and they will have to defend themselves against him, Professor Umbridge gives him detention for telling lies.
Professor Umbridge also gets herself appointed Hogwarts High Inquisitor, with the right to start overseeing each professor's lessons at the school. She uses her power to get Sibyll Trelawney, the (admittedly terrible) Divination professor fired; she also uses her authority to send Aurors after Hagrid, since she hates half-humans and Hagrid is half-giant. She appoints Malfoy and his goons to an "Inquisitorial Squad" to spy on his fellow students, and she uses this squad to root out Harry's D.A. (Defense Association/Dumbledore's Army) because she is afraid of any student groups outside of her direct control. When Dumbledore claims that the D.A. was his idea and leaves the school suddenly, Professor Umbridge becomes Headmaster Umbridge, as she has always wanted.
The point of all of this is to show Professor Umbridge's main characteristic: she is power-hungry and ambitious. Her love of power is apparent and completely disgusting: when she has Harry in detention, she makes him write, "I must not tell lies" (13.154) over and over with a Blood Quill that makes his hand bleed. When she inspects his bleeding hand, she smiles and tells him to come back for more the next night.
When she manages to throw Sibyll Trlawney out of the castle, she sounds "callously amused" (25.230) as she stands over Trelawney. Harry is "revolted to see the enjoyment stretching her toadlike face as she watched Professor Trelawney sink, sobbing uncontrollable, onto one of her trunks" (25.232).
Finally, when Professor Umbridge works herself up to casting a Cruciatus Curse on Harry to find out what he's up to, Harry notices "a nasty, eager, excited look on her face that Harry had never seen before" (32.199). She loves to lord it over people who are weaker than her, and she enjoys causing emotional and physical pain.
Professor Umbridge's love of authority makes an important point: the problem with power is that it often attracts bullies. It doesn't matter if it's the Ministry of Magic or Voldemort, all power corrupts. Even though Professor Umbridge is supposedly on the good side, working with the government to defend the British wizarding world, her real agenda is to establish herself as the unquestioned Head of Hogwarts. She wants to have total control on everything going on around her, and she can't tolerate any independent thought.
Professor Umbridge's extreme control-freak tendencies put her at odds not only with Hogwarts students, but also with all of her fellow teachers. She manages to get into a shouting match with Professor McGonagall over Harry's chances at being appointed as an Auror by the Ministry of Magic. When Fred and George, the twin troublemaking Weasleys, make a swamp out of the fifth floor hallway, Professor Flitwick, the Charms teacher, pretends he can't get rid of it. She can't hold the school together once Professor Dumbledore is gone because she has managed make everyone totally hate her.
Indeed, the castle itself rises up against her, refusing to let her into the office of Professor Dumbledore once he leaves the school under suspicion of treason against the Ministry of Magic. For all that she pretends to play by the rules, she is a sneak and a liar, and not one stone of Hogwarts helps her keep control of the school as both teachers and students stand against her bullying ways.
When we finally find out, by the end of the novel, that it was Professor Umbridge who ordered two dementors to go to Little Whinging and find Harry Potter, it's the last straw. But we have known that she was evil since she first used the Blood Quill to make Harry write out, "I must not tell lies" (13.154). Professor Umbridge is one of the most horrible villains in the entire Harry Potter series, and the thing that makes her worst of all is that she hides behind a mask of respectability and honor. But behind that mask, she's no better than any of the Death Eaters working for Voldemort.
One last note about Professor Umbridge: in addition to all of her many, many other flaws, she also has a deep loathing for all half-humans. As a result, she sets out to get Hagrid out of Hogwarts as soon as she can. But her hatred of half-humans also proves to be her undoing: when Hermione lures Professor Umbridge into the Forbidden Forest, she shrieks horribly offensive things at a whole herd of centaurs, and they do not respond in a kindly fashion. Professor Umbridge is so certain of her own power and authority that she doesn't even bother to be careful – with the result that she manages to get trampled before being thrown out of the Forest.
Have you ever heard the expression, "pride goes before a fall?" It means that people who get overconfident tend to trip because of it. Professor Umbridge is a classic example: she builds herself so high that, when she falls, she tumbles far: after the return of Dumbledore, as she tries to sneak out of the school where she was briefly headmistress, Peeves the poltergeist chases her off the grounds while whacking her with a walking stick and a sock full of chalk. Now that's an embarrassing way to leave a former workplace. But we can't think of anyone who deserves the humiliation more than Dolores Jane Umbridge.