The German army moved across Europe in an attempt to subjugate Europe. First they captured Poland; then they took the Netherlands, Belgium, Denmark, Norway and France. Italy, an ally of Germany, attacked Greece and the Balkins, and in March and April of 1940, Germany occupied Yugoslavia and Greece.
However, though some online sites mention that the German did try to invade England by sea, there seems to be a greater consensus that the Nazis never did so. The reasons given were the strength of the British Royal Navy and England's ability to resist air attacks by the Germans.
Hitler did not attempt to invade England on account of the strength of the British navy, and England could not be put down by air attacks. England won "the battle for England" in the air.
That is not to say that Hitler did not entertain the idea of trying to invade England. During 1940-41, Hitler did, in fact, prepare for a British invasion, but plans ended when:
Hermann Göring's Luftwaffe [German Air Force] failed to gain air superiority over the Royal Air Force in the Battle of Britain.
The German's air campaign against Britain occurred during the summer and fall of 1940. The objective was to:
...gain air superiority over the Royal Air Force (RAF), especially Fighter Command.
England's Prime Minister, Winston Churchill, delivered his famous speech which gave this decisive battle its name:
The Battle of France is over. I expect the Battle of Britain is about to begin...
The Battle of Britain was fought entirely in the air. The Germans targeted areas they felt would force the English to surrender, including shipping convoys and centers, RAF airfields, aircraft factories, and finally, ground infrastructures (roads, water supplies, etc.). The Germans then shifted their attention to bombing "areas of political significance," using "terror bombing tactics."
Germany's failure to force England's hand is considered the Nazi's first major defeat, as well as a critical turning point in the war. Had the Germans been successful...
Hitler might have launched Operation Sea Lion, an amphibious and airborne invasion of Britain.
THE BATTLE OF BRITAIN
Hitler's ultimate goal was to invade and subdue Great Britain, which would have given him control of nearly all of Europe. He already had plans drawn up for Operation Sea Lion, a combined amphibious and airborne invasion, and after the fall of Paris, he set his sights toward this goal. Hitler's primary objective at that point was invading and capturing the Soviet Union, and he expected England to eventually surrender with little other Allied support. But when he realized that the island nation planned to go on alone if necessary, Hitler decided to pursue his goal. First, needed to gain superiority in the air, and so began the Battle of Britain.
The Battle of Britain had been predicted by Winston Churchill shortly after France fell, and England quickly assembled its aircraft to meet the expected attack. The German Luftwaffe and the British Royal Air Force met each other for more than four months between July and early November 1940. The Luftwaffe began by attacking strategic naval ports, such as Portsmouth, and later concentrated on RAF bases. To Hitler's credit, his orders at first did not include deliberate attacks on civilian areas although political areas and terror strikes became commonplace later.
The powerful Luftwaffe had gained air superiority throughout Europe, but it had been created as support for Germany's ground forces. This time they would go it alone, and they were not up to the task. They expected to control the skies over Southern England within four days, and the operation hoped to defeat RAF resistance within a month. Instead, the RAF strategy of breaking up Luftwaffe raids was aided by an early form of radar which often detected German attacks that were met by RAF defenders. The Luftwaffe also had to deal with the long flights which left many of their planes low on fuel and unable to complete their missions.
During the four months of air battles, the Luftwaffe lost nearly 75% of their aircraft engaged (approximately 2550) and suffered more than 4000 casualties. A similar percentage of RAF planes were downed of their nearly 2000 aircraft engaged, but crewmen losses were less than 1000. The Battle of Britain proved to be a decisive victory for the English and the first major defeat for Germany. Hitler's plan to invade England was put on hold--permanently.