The assasination took place in Sarajevo, the Bosnian capital. Originally, the assasination was tried just after 10am June 28, 1914 with a Grenade, as the heir to the Austria-Hungary throne was paraded around the city. The grenade missed the Archduke, however it hurt several of his man.
The following events, occurring later the same day, are still not entirely clear. Some say the Archduke was persuaded to leave the city as soon as possible, and was leaving, others say he wanted to visit his men in hospital. Either way, the Archduke and his wife were in their car, and had apparently taken a slightly wrong turn. The driver realising this, stopped to reverse, unfortunately in front of one of the members of the assassination conspiracy. Shots were fired from short range, and the Archduke and his wife both died shortly after.
The assassination was then the final straw for Austria-Hungary, who were already unhappy with Serbia, and had previously had some disagreements. When Serbia rejected some of Austria-Hungary's demands, the A-H Empire declared war against Serbia on July 28, 1914. Russia and France were obligated to mobilize their armies if any of the Triple Alliance mobilized (Secret Treaty of 1892), and so they chose their sides and joined the War.
The bottom line is that the World War was triggered by the Archduke's assassination. It is, however, highly likely that some other event would have triggered a European War had it not been for the assassination. Difficulties within Europe were mounting and tension was generally high, and rising.