First appearance on page 156 of the first book.
In the first book, Ron goes to Madam Pomfrey after being bitten by Norbert, a baby dragon. Ron told her she bitten by a dog, as truthfully saying dragon, would incriminate Hagrid. After Harry fought Professor Quirrell in the dungeons, he spent three days unconscious in the hospital wing. Madam Pomfrey was reluctant for Harry to have visitors(particularly Ron and Hermione.)
Madam Pomfrey helps Harry in the second book by regrowing his bones on his arm because Dobby the house elf broke it with a bludger. She also helps many other people in the second book. She regrows bones, fixes arms, and unpetrifies people. After Dolores Umbridge stunned Minerva McGonagall for no reason at all, except to get her out of the way, in the fifth book, Madam Pomfrey said she would resign in protest, if she weren't afraid of what would become of the students without her.
Madam Pomfrey didn't appear in the film adaption of Harry Potter and the Philosopher's Stone, but does appear in the film adaption of the second book, where she is played by Gemma Jones.