There is nothing like practice. I am glad that my many, many, many pieces of juvenilia were handwritten -- in my virtually illegible hand-writing no less -- but it was good practice all the same.
The first trick is to always change the names. Besides the psychological effect of making them your characters, besides the legal effect of escaping copyright, names have baggage. You may find that Catherine has dark hair, which will change the heroine's hair all on its own. (You can't count on the reader picking up your baggage, but you can find it useful if you write it in.)
It can be like prying a gemstone out of a rock. You may have to take several stabs at it -- put it down and come back a few days later, when you have more distance between you and the original story. It may feel like it can't be done, because the original story all hangs together. But it's a necessary step.
And then you start to look at what else you can change without changing what interested you in the first place.
Even with the names and trivia, it can be hard. Part of that is lack of practice, part of it is that in a good story, all these trivial pieces are integral, and part of it is that even trivia has a ripple effect. Drastic changes in name for instance -- from Jill to Euphrosyne -- imply changes in her parents and her culture.
And as you get better, stretch your changes. See how much you can change, and see how the changes ripple. Poor or rich? It will make a big difference. On this planet, or on another, on a spacestation, in a fantasy land. With a different kind of magic.
Take, oh, let us suppose that you want to write a story about an orphaned boy with a magical legacy raised by his aunt and uncle and mistreated by them, who one day has to learn about his legacy.
You could consider whether it was needed. Whether you could be happy with writing about a boy raised by his parents and doing well enough. It would, on one hand, save some specialness you could expend later, without turning him to a Mary Sue then. On the other hand, you want to make your character special somehow; Joe Nobody is as dull as Mary Sue. And the situation has plot potential. And you never want to just file off the serial numbers. You want to engrave your own on the story.
You can also brainstorm with each of the ideas. If we break it down:
Why else could a boy not be raised by his parents? Perhaps they vanished. Perhaps they have jobs that need a lot of travel. Perhaps they -- are in jail. (And then the questions arise: were they framed? Was it real but in a good cause (perhaps in an unjust foreign country? Were they just crooks? The first two have more straightforward plot potential, but the third has a great deal of drama.)
"boy" -- or girl?
"by his aunt and uncle"
Grandparents could also feature. Or an much older sibling. Or even a not much older sibling.
"and mistreated by them."
There's a lot of ways he could be mistreated. Perhaps he could be suffocated. Or perhaps he cold be just neglected and allowed to run wild.
And see what strikes the fancy:
Mortimer, who was born very late to his parents, who vanished when he was twelve. His older brother had to return to the family estate because of the conditions on its inheritance (magical conditions?), and resented very much leaving the city. He pays no more attention to Mortimer than he strictly must, and Mortimer is running wild in the woods. And learning things that would surprise his brother very much.
Sally's parents were arrested in a foreign country when they stole back a vital magical artifact. Her mother's parents took her in but were both thoroughly ashamed of their daughter and son-in-law and very afraid that Sally would emulate them. They shelter her until they almost smother her. They try to keep her from learning magic, but they haven't checked all the chests that were stored in the attic.