The justices vote and someone is selected to write the majority opinion. That justice drafts the opinion and shares it with at least the other ones in the majority, maybe all the justices, until the opinion satisfies enough that a majority subscribes their names to it. Sometimes a majority voting justice will concur with the opinion but add a personal opinion to make additional point(s). Dissenting justices write their own opinion and go through the same process, sharing it with other dissenters at least, and maybe all the justices. If you read Supreme decisions, it is common to see concurring opinion address the dissenting opinion points and dissenting opinions commenting on the majority decision points.
And if it was Sotomayor who leaked the draft she ought to be impeached.