I voted “Wouldn’t have done it at all”. Germany, traditionally a land power, was in no position to improvise in a few weeks (or even a few months) a cross-Channel invasion that – by way of comparison – took two major naval powers (the US and the UK) more than two years to plan and prepare. The Wehrmacht was skilled at river crossings, and thus was inclined to view a cross-channel invasion as just a large version of a river crossing, but this was simplistic thinking at best. Rivers aren’t subject to the tidal and weather factors that have to be taken into consideration when dealing with the English Channel (which is a notoriously unpredictable stretch of water). Moreover these tidal and weather factors, when combined with the Channel’s width, meant that the Germans would not have been able to use two valuable river-crossing techniques: laying down artillery support from one bank to another, and building assault bridges (for example pontoon-type bridges).
If I’d been able to dictate German strategy after the fall of France, my plan would have been to strangle Britain directly by sea and indirectly by land rather than trying to invade it. By “directly by sea” I mean devoting more of my resources to the U-boat elements of the Battle of the Atlantic. By “indirectly by land” I mean using the Wehrmacht to pinch off Britain’s shortest route to India, the Far East and Australia: the Mediterranean. A step in that direction would have been to take Gibraltar, which overlooked the western entrance into the Mediterranean. When France fell, the bulk of the Wehrmacht was nicely positioned to strike south through Spain towards Gibraltar. Hitler had some talks with Franco along these lines, but they went nowhere. Given Spain’s weak economic and military situation after the Spanish Civil War, Hitler could simply have given Franco three choices: join us in a war against Britain; stay nominally neutral but allow the German Army to traverse Spain (which is more or less what Japan said to Thailand on December 8, 1941); or resist and be conquered by Germany as the Wehrmacht strikes towards Gibraltar.
With Gibraltar in German hands (reinforced by naval units from Italy), British access to the Mediterranean would have been appreciably complicated, and the British position in the Mediterranean basin would have been weakened. The next thing I would have done was to try take control of the Suez Canal away from Britain. This would have involved a two-pronged offensive. German forces would have been sent (via Italy and the Mediterranean) to Italian-controlled Libya, as was done historically with the Afrika Korps, and these forces would have teamed up with the Italians to attack Egypt from the west. In parallel, German forces would have been positioned for a strike into the Balkans, then Turkey, from which they would have attacked through the Levant towards Suez and Egypt from the east. Once Egypt and Suez were under my control, I’d have tried to pick up Iraq and Iran while in was in the area, to acquire their oil (and deprive Britain of it at the same time) and to position my forces on the Soviet Union’s south-west flank,
All of these operations would essentially have been land-based ones, therefore much more within the capabilities of the Wehrmacht than a cross-Channel invasion. They wouldn’t have knocked Britain out of the war quickly – and perhaps not at all – but theyt would have weakened Britain much more than the actions which Germany actually took in the year between the fall of France and the start of Barbarossa.