So this is two part question I hope someone who was alive in that time could answer
There were three narrow air corridors between West Germany and West Berlin. These were restricted to Allied (US, British, French) civil and military aircraft. I believe only Pan Am, Air France, and BOAC flights were allowed, although Lufthansa partnered with Air France to get their passengers in and out of West Berlin. Aircraft were restricted to 9500 ft, and were not allowed to overtake. There were regular flights in and out of Berlin, just like any other city.
For most of the Cold War, there were also a handful of road, rail, and river transportation links. The border crossing at Helmstedt-Marienborn on the Hanover-Berlin autobahn was the largest, and named Checkpoint Alpha. Travelers were stopped by Allied guards, their vehicles inspected, and they were briefed on how the crossing was conducted. Stopping was only allowed in emergencies, and Allied tow trucks patrolled the road to retrieve stranded motorists. Contact with East Germans was strictly forbidden, except polizei (and even then you were only to roll the window down a bit). The car was then inspected by East German border guards. At the Berlin end of the autobahn, Checkpoint Bravo, cars were again inspected (with mirrors looking for stowaways under the car) by East German guards, then by Allied guards, and then you were free to enter West Berlin. Train travel required similar inspections at each end.
By the 1980s, additional crossings were opened, particularly for West Germans visiting East Germans, and trucks bringing goods in and out.