Initially, contacts between East and West were very troubled when the Berlin Wall went up in 1961. Not only did the Communist Party forbid citizens to travel to the West, but West-Germany pursued a foreign policy doctrine that rejected any recognition of East-Germany and therefore refused all forms of cooperation (which would be required for mail service). Of course there were ways to circumvent this by making use of countries that both East- and West-Germany did have diplomatic relations with.

From the late 1960's, Chancellor Willy Brandt, former mayor of West-Berlin, pursued a policy of "Ostpolitik", intended as a long term strategy towards re-unification through "popular diplomacy". He believed that by gradually restoring economic, cultural and political relations with East-Germany, the East-German regime would gradually lose its grip on the thoughts of its population, that would come into contact with regular West-Germans. In the long run, the East-German people would simply stop believing East-German propaganda.

As a result, both Germany's signed their first treaties in 1970 and established diplomatic recognition. Families were re-united, travel restrictions eased, and joint economic projects established. Throughout the 1970's and 1980's, this became something of a bargaining chip. West-Germany promised more investments for good behaviour, and East-Germany restricted or relaxed travel restrictions depending on their mood.

In general, only "reliable" citizens could travel from East to West. For Westerners it was somewhat easier to visit family in East-Germany, provided they were not actively campaigning against East-Germany. Many people maintained contact through writing letters, but these were routinely scanned and intercepted by the Stasi for forbidden political contents or to uncover espionage communication.

Most problematic for East-Germany was that many of its citizens could receive West-German radio and television. For example, when Soviet leader Brezhnev planned to visit West-Germany in 1977, the KGB and Stasi informally warned West-German politicians that it would be unwise if West-German television proceeded to broadcast a "provocative" film about the Prague Spring in Czechoslovakia, called At Noon on Red Square. In case they failed to pursuade the West from refraining to broadcast it, the GDR should prepare "distracting programs" to be broadcasted simultaneously. They ended up doing this, showing a Swedish international hit, and proudly concluded a majority of East Germans had watched this instead of the West-German "anti Soviet" film.

The Radio Free Europe headquarters in West-Germany was bombed in 1981 by Carlos the Jackal, probably on the orders of the Romanian secret police according to assesments by the Hungarian and Czechoslovak intelligence services.

From 1989 onwards, East-Germany gave in to Soviet pressures to liberalize itself. When Hungary opened the iron curtain, thousands of East-Germans travelled freely to the West through Hungary, eventually forcing the East-German politburo to take a rash decision to "suspend travel restrictions immediately". A journalist asked the regime when this would go into effect, and the unprepared spokesman said "as far as I know from now". That evening, East and West Germans were cheering on top of the Berlin Wall and breaking it open. East-Germany ceased to exist after 1990.

I hope this answers your question.

Recommended reading:

Odd Arne Westad & Melvyn Leffler, "The Cambridge History of the Cold War" Vols I, II, III

Mary Elise Sarotte, "Dealing with the Devil: East Germany, Detente, & Ostpolitik 1969-1973"

Jens Gieseke, "The History of the Stasi"

Kristina Spohr, "The Global Chancellor: Helmut Schmidt and the reshaping of the international order"

Heinrich August Winkler, "Germany: the long road West 1933-1990"