By June of 1940, the Germans had occupied most of Europe and began to set their sights on Britain. Their plan was to first have their Air Force destroy the British Royal Air Force (RAF) and then, once they had air superiority, to have their Army actually invade Britain if the British did not sign a surrender agreement.
The attempt by the Germans to destroy the RAF was known as the "Battle of Britain". It began in early July, 1940 with attacks on Allied shipping in the English Channel. These early attacks gave the Germans a chance to become familiar with RAF air defenses.
In early August the Germans began extensive attacks on British air fields and these attacks continued with increasing intensity until early September, with the Germans still unable to defeat the RAF. There were a number of reasons why the Germans were unable to defeat the RAF, among them being:
1) The Germans did not understand the functioning and effectiveness of the British radar defense system and so they made little effort to destroy the radar towers. The radar system gave the British the ability to put fighters quickly into the air to meet the incoming German planes. The Germans destroyed some of the radar towers, but they were always quickly replaced and the Germans made little effort to return and bomb them again, thinking that they were not really important military targets.
2) The British were good at camouflaging their air fields and aircraft on the ground so that the Germans could never get an accurate count of remaining British aircraft by studying reconnaissance photographs. At one point the Germans thought that the British had only 50 fighters left while they actually had over 600 remaining.
3) The British were manufacturing new fighter aircraft at a rapid rate of over 400 per month, and airmen from the Commonwealth countries (Australia, Canada, New Zealand, Rhodesia, South Africa) and German-occupied countries, such as Poland and France, were recruited to help man the new planes to replace some of the British airmen who were lost in battle.
On September 7 the Germans switched tactics and, instead of continuing to bomb airfields, began launching large bombing raids against London, beginning an extended period of bombing of British cities known as the "Blitz". It was the Germans' hope that the British people would become demoralized by the intensive bombing and force their government to sign a surrender agreement with Germany. This tactic did not work -- the attacks only increased the resolve of the British people to continue to fight. The Germans soon postponed their attempt to conquer Britain and turned their sights on the Soviet Union. However, they continued to bomb London and other British cities throughout the winter of 1940/41 and at one point bombed London for 76 straight nights. The bombing campaign that winter killed about 30,000 civilians.
Below is a 5-part video that tells the story of the Battle of Britain:
Below is a 6-part video covering the British RAF's contribution to the bombing offensive against Germany during WW2:
Below is a 4-part documentary video which gives a good summary of the events leading up to World War II in Europe and also summarizes the events of the war itself. It starts with World War I and its aftermath and ends with the defeat of the Nazis in 1945.