"When my sister was six years old, she was attacked, set upon, by three Muggle boys ... It destroyed her, what they did: She was never right again."
--Aberforth Dumbledore (DH28)
When Ariana Dumbledore was six years old, three muggle boys saw her doing underage magic. They demanded she show them what she was doing, and when she couldn’t, they attacked her. The event traumatized her, and led to the unraveling of the Dumbledore family.
Given that Ariana was six, and she was born in either late 1884 or early 1885, that would place this attack either at the end of 1890 or the first half of 1891. Percival Dumbledore was sentenced to Azkaban "scarcely a year" (DH2) before September 1892 (when Albus started Hogwarts), so it's likely the attack happened in 1891.
Note that we are explicitly told that three boys attacked Ariana for being a witch. This is all an interesting inversion of some historic accounts of people allegedly cursed by witches, such as those thought to be victims of the Salem witches. The infamous witch hysteria in Salem began in response to three young girls exhibiting disturbed behavior and experiencing powerful, violent fits that were blamed on witchcraft (source: Wikipedia). Another example is that of Anne Gunter, a young woman who feigned very similar symptoms. Three women were accused of being witches and having cursed her (source: Witches: A Century of Murder, a History Channel documentary). -BB