There's really only one way to do it.
We trade ourselves below the apron offering Portland pretty much whatever they want out of the bucket of Anderson Varejao, Tristan Thompson, Iman Shumpert, JR Smith, Delly, our picks, and Brendan Haywood.
Obviously there would be restrictions on that (as in, you can't take both Shump and Smith), but in general the way to get Aldridge is to (1): convince him that he can play center in our lineup for 24 minutes a game (GSW winning without a center should help that case); (2): convince him to tell Portland he either S&Ts to Cleveland or he walks to San Antonio (or elsewhere).
That's how it gets done. But it's a tall order and means Thompson and Varejao must go (Varejao need not be traded, he can be stretch waived - but trading him is preferable).