What started Seven Years War?
Austria was mad at Prussia because Prussia "stole" Silesia in the previous war, the War of Austrian Succession. That previous war was started partly because the leader of Austria, Maria Theresa, was a woman and perceived as weak.
So in the years between the two wars, Maria Theresa re-organized the Austrian army, got alliances from France and Russia, and decided to attack.
Great Britain was an ally of Prussia and France was an ally of Austria. Great Britain and France already were mad at each other over their competition to get colonies in North America, so it didn't take much for them to fight.