I’m assuming that it’s not THE Case-Shiller algorithm, as that must be proprietary stuff,

Here’s a good description of their algorithm. It’s missing some implementation details but it’s almost complete.

http://www2.standardandpoors.com/spf/pdf/index/SPCS_MetroArea_HomePrices_Methodology.pdf

if I buy a crummy little house in bird rock, for a million, tear it down and build a much bigger house and sell it for two million, will Case Shiller report a 100% price increase on this house?

They exclude houses with substantial physical changes if they can detect them in deed records. They also try to detect “unusual” price changes and either exclude them or assign lower weights to them.