As you have speculated, the Berlin Wall did in fact encircle the entirety of West Berlin. It was much easier to travel in and out of West Berlin than waiting for an airplane, however. You could ride a train or even drive (you needed the proper documentation to drive through East Germany) to West Germany from West Berlin, and trains were the primary supplier of goods to West Berlin. The trains did not service East Germany, but rather drove straight through on their way to and from West Berlin (they could and would be stopped by East Germany border guards, however). Remember, the point of the Wall was to keep East Berliners from escaping to the West, and so the East German government did not bother to stop this kind of travel between West Germany and West Berlin. The failed Berlin Blockade of 1948-1949, when the Soviets did attempt to cut off West Berlin from the world only to have the West embarrass the East by providing a constant supply of goods through the round-the-clock Berlin Airlift, had already decided that battle. West Berlin would stay a part of the West (technically occupied by the Americans, British, and French), but the Soviets could at least prevent East Germans from leaving by simply crossing the border into the Western zone of Berlin, although the need to build a wall obviously damaged the prestige of the Eastern Bloc.