The physical part of how Darth Vader died was by Force lightning. As Darth Sidious attacked Vader's son, Luke, Vader suddenly rejoined the light side of the Force, and lifted Sidious up, and threw him down the Death Star's reactor shaft, but in doing so, the lightning damaged his own suit, which was crucial to his survival. He ended up dying while looking into his son's eyes, as he vanished into the light side of the Force.