Whose assassination instigated war between Serbia and Austria-Hungary?
Archduke Franz Ferdinand.
Archduke Franz Ferdinand's murder was what began the war between Serbia and Austria-Hungary that was declared July 28, 1914, 1 month to the day after the presumptive heir to the Austro-Hungarian throne was killed.
This declaration of war, led to the mobilisation of the Russian Empire's troops to defend its friend; The Kingdom of Serbia, and so declared war on the Austro-Hungarians- the World War 1 to an extent had now begun.
In response to this declaration, the German Empire, who were allied and had developed a pact with the Austro-Hungarians, declared war on the Russians in a sign of friendship with its ally.
All this did was instead pull the French in, who made a pact with the Russians, that if the Germans declared war on them, they would come to their aid.
At this point, the British had not yet declared war, due to their Royal Family being related to the German Royal Family, but did support the French and Russians-
It was when the Germans performed the schlieffen plan- which was the plan to invade France through Belgium, bypassing its defences on the German border, to which it would quickly swing through and capture Paris and defeat the French army, in time for the majority of the German army to return to defend Germany's eastern border against the (thought to be) slow, but large, Russian army.
They found when they did go through Belgium, the Belgians did not fall as easily as planned, and held the Germans up, this invasion of Belgium also 'activated' the alliance Britain had with Belgium, as well as Britain's ports/navy becoming threatened due to this occupation of Belgium, did they then mobilise its small, but effective army, the British Expeditionary Force (BEF), and with the Belgians and some French, slow down the German advance.
The Russians, however had responded quicker than the Germans had anticipated, meaning they had to dedicate atleast half of their forces to defend their east flank, which slowed down their progress in Belgium and France.
This then steadily turned into a deadlock of trenches and attrition, in which over 4 years of fight would ensure.
Hope this helps, as well as the break down of how this led to the world wide, crippling conflict; World War 1.