The war ended in Europe on May 8th 1945 (VE Day) after Germany surrendered unconditionally.
All hostilities of war ended on August 15th 1945 (VJ Day) after Japan surrendered unconditionally.
Here is a downloadable .pdf file which lists the main events of the war. Chronology of WWII.
The evacuation of allied troops from Dunkirk took place in 1940, between May 26th June 3rd. British, French and Belgian troops were evacuated from the French coast, because they had been surrounded by advancing German troops.
The Battle of Britain was a large-scale attack on Great Britain by Nazi Germany's Luftwaffe. It has been described as the first major military campaign fought entirely by air forces. It is recorded as having lasted from August 8th to October 31st 1940, although there were heavy bombing raids on Coventry, Manchester, Liverpool, Clydebank, London and Hull during 1941.
D-Day was 6th June 1944 and was part of "Operation Overlord". This was the day the allies started the final push to end the war in Europe, beginning with a massive landing of men and machinery with considerable assistance from the Americans. This map shows the names used for the Normandy beaches.
Different countries joined the war at different times. The British forces were part of The Allies. The German support came from The Axis. Here is a list of those countries that aligned for either side. Axis v. Allies.