Pare it down to the essential core of what it is that is so interesting and then build up with details that are different from the original. Possibly even deliberately selected to be as different as possible. . . (I pontificate about it at great length here.)
The funny thing is when I have done so, to the point where the original story couldn't be identified if you didn't know, but am slogging along on the story, or switching to another because this one is dry, I can still sometimes restart it by re-reading the story I originally ripped off. It reminds me of what the tiny little bit was that I found so interesting that I wanted to steal it.