Question

how did the assasination of archduke ferdidnand lead to ww1

Answer 1

this should cover it in really good depth http://www.history.com/this-day-in-history/archduke-franz-ferdinand-assassinated

Answer 2

Everybody had treaties with everybody else in Europe. The idea was that nobody would attack anybody else because of the treaties. But Germany wanted to invade the low lands and France. They would start with Lichtenstein because they needed an easy first round opponent.
But there were the treaties.
Ferd was riding around Sarajevo with the top down showing off because he would become leader of Austria-Hungary. He got shot.
Germany figured that was a good enough excuse to go for France.
Everybody pointed fingers at everybody else. They decided which treaties to keep and which to ignore. So the whole system to prevent war created the setup for WWI.