The Archduke was killed, along with his wife, by Gavrilo Princip, a Serbian nationalist protesting Austria's claims on Sarajevo and the rest of Bosnia, territories the Serbs believed were rightfully theirs. (PROSE: Human Nature) According to the Tenth Doctor, at the moment of the assassination, he was wearing a funny hat. (COMIC: The Weeping Angels of Mons)
Unbeknownst to the general populace, however, the start of the war was influenced by the passage of the Nemesis statue around Earth in November 1913, (TV: Silver Nemesis) with the Archduke's assassination being the event which triggered the conflict.
While investigating the Dalek Project, the Eleventh Doctor grew fearful as he began to suspect that the Daleks had engineered the assassination of Ferdinand and his wife by conditioning Princip to kill them and thus plunge the world into war, although his suspicions were never confirmed. (COMIC: The Dalek Project)