Were there formal border crossings or a 'wall' between East Germany and the Czechoslovak Socialist Republic during the Cold War? Would it have been relatively easy for someone from East Germany to travel to the other socialist state or would they have needed to apply for a visa / go through inspection at the border before they could travel?
For citizens of the GDR (German Democratic Republic), foreign countries were divided into two categories: 1) 'Socialist Countries' and 2) 'Not Socialist Countries'.
Between the GDR and the CSSR there was a formal border crossing, but no special visas were required. What was somewhat difficult was changing money, which could be done in certain amounts. No country wanted the worthless currency of the other country. If one had D-Mark (which was the de-facto hard currency), then one could easily change on the black market.
Citizens of the GDR living near the CSSR would make unofficial 'shopping trips' into the CSSR to buy certain goods which were cheaper or even available. But one had to be discreet about such shopping trips.
For Poland, there were no strict visa regulations until 1980. After 1980 the visa process for Poland became very complicated. Other fellow Socialist countries, like Hungary, Romania and Bulgaria were visited as summer holiday destinations. Of these countries, Hungary was very expensive for GDR citizens but the most interesting.
As mentioned before, the biggest headache for traveling abroad for GDR citizens was the currency exchange -- GDR citizens were only allowed to exchange a certain amount of money every year. To avoid such headaches, many just took their summer holidays in the GDR itself. Many state-owned companies provided their workers with summer holiday accommodation as well.
Traveling to 'Not Socialist Countries' was far more complicated and involved a long visa process.
Recommended reading (in German): 'Urlaub vom Staat: Tourismus in der DDR'. (C. Goerlich).
There was no special permission required for Czechoslovaks during the Communist era to travel to other Eastern Bloc countries, including the GDR. This does not mean, however, that one could just waltz across the border, which was certainly patrolled, although not barbed-wired to the extent that the borders with West Germany or Austria were. Definitely not some kind of socialist Schengen area. It is probably fair to say that the purpose of those borders were to deter smugglers rather than emigrants. Czechoslovaks traveled to the GDR quite frequently, usually on trips organized by one of the state travel agencies, which would organize all the necessary documents for them.