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.