What did Uchiha Madara do to Obito with the Black Zetsu?
He switched life forces with Obito. That's why he said: "Let's switch". Obito is probably still alive because of the Kyuubi foreshadowing that the Jinchuuriki of the Ten Tails has bigger life force than other Jinchuuriki's.

Madara is revived by Black Zetsu controlling Obito using Gedo: Rinne Tensei!