She read it in a magazine. A Muggle magazine.
Which she never would have admitted to reading, but it was just lying there. And it held a mish-mash of truth and lies, from "crystals make your garden grow" to "how herbal teas are the new healing power." But Dolores, newest member of the Ministry of Magic, picked the magazine up while it was open to a page of the most adorable kitten pictures - and a heading that read "Cats can increase your powers."
Dolores glanced at it a second time. Under the large and lurid heading, paragraphs about "Feline Focussing of your Aura" and "Cats Concentrate your Conjuring Powers" enlarged upon the concept, with more enticing pictures of cute kitties playing with crystal balls...
Of course she'd never admit to believing in that Muggle rubbish. After all, it wasn't her job to keep an eye on the Muggle's perception of the world of Magic, and let the higher-ups know if anything that was actually trueturned up on the news or in their papers. There was another department looking after that. Her job was utterly boring, so she slipped the magazine into her pocket and read it in her lunchbreak. And on the way home that night, she bought the tabby kitten she'd been admiring in the window of the Magical Menagerie, and that very night she sat the kitten on her pink armchair, and for the first time managed to Transfigure her stale sandwich into a cupcake with sprinkles.
But if one cat could augment her powers sufficiently to help her with spells...
The next night Dolores brought home a black-and-white mewling critter, and as the two kittens played "catch" around her lounge, she giggled with girlish glee as she cast handfuls of sparkling stars that floated gently to the carpet and vanished as the kittens pounced on them.
By the end of the week, though, Dolores was discovering the disadvantages in having five (Five? When had it grown to five? Surely she'd only bought one more at the store, and then there was that stray she'd found in a back alley, and the one that had followed her...) kittens around her home. The food was costing her a fortune, and not all of them had been housetrained. She found her work stockings shredded (although Mipsy the first kitten had looked so very adorable in the middle of them so Dolores hadn't the heart to scold her), and the curtains were showing severe signs of wear. She now had to eat standing up, because if she sat down for three seconds, all of the cats were fighting over possession of her lap.
But she'd managed the best magic she'd had all week. She'd been trying for a Patronus, and there had been a little gleam, just a small one, at the end of her wand. She was sure of it. Maybe just one more cat.
Two months later, Amelia Bones sat opposite Dolores in a small room at the Ministry, a brazier of incense reducing the strong stench of tomcat urine that permeated all of Dolores' clothes. The probationer was in tears, sobbing incoherently, while Amelia read through the case notes in sombre silence.
After a while, she put the parchment down and looked at the pathetic woman opposite.
"You realise, don't you Dolores, that forty-seven cats is more than one person can manage on their own? That we'll have to take them from you, especially as they're now starving, flea-ridden and in very poor condition?"
Dolores sobbed even louder, words such as "My babies!" and "My spells" barely recognisable through the blubbering. Amelia grimaced, then glanced down at the pictures of the kittens attached to the parchment. Many of them were down to skin and bones, and it wasn't even certain if all of them could be saved. But maybe there was another way to let this woman, this poor, deluded young woman who obviously cared about her kittens, to keep them somehow ...
The surfaces had all been draped in lacy covers and cloths. There were several vases full of dried flowers, each one residing on its own doily, and on one of the walls was a collection of forty-seven ornamental plates, each decorated with a large technicolour kitten wearing a different bow around its neck...
Disclaimer: JKR has a wicked imagination and owns all these characters, even the cats. Last paragraph from HP:OTP, except for the italics which are mine.