I'm not sure how closed off information sources were other than you couldn't buy rock records.
Glad to see a timeline put on your question! It helps a lot.
The short answer is that access to all media was intentionally limited and foreign media especially so, except in specific cases. The state wanted to intentionally control access to information for political but also for social/cultural reasons-- so whether that was preventing people from getting exposed to messages of religious-focused martyrdom or anti-Soviet political messages, they wanted the lid clamped down tight.
Even in the age of Lenin, art was understood as powerful for the cause of Communism but also dangerous if used in pursuit of other ends. From "Attacks on Intelligensia":
Communist Party ideology influenced the creative process from the moment of artistic inspiration. The party, in effect, served as the artist's Muse. In 1932 the party established socialist realism as the only acceptable aesthetic—measuring merit by the degree to which a work contributed to building socialism among the masses. The Union of Writers was created the same year to harness writers to the Marxist-Leninist cause.
In the USSR, the stakes for art are high. It has to support the politics, it has to support the state's stated aesthetic, and it has to be supportive of a vision of Soviet life that is unlikely to rabble-rouse or stir up conflict. That means that ensuring art did not fall into the wrong hands-- like the hands of your hypothetical Soviet reader who is just hoping to brush up on some Agatha Christie-- is critical.
How did they do it? Government agencies.
Establishment of the Censorship Agencies
The period from 1922 until 1953 had absolutely repressive Soviet censorship, from Stalinism until the reforms brought in under Khrushchev and his "Khrushchev Thaw." The agencies were Goskomizdat (censorship of writing), Goskino (censorship of film) and Gosteleradio (censorship of radio and later, television.)
During this early period, first-hand accounts of the Bolshevik revolution-- ostensibly talking about the glory of the Soviet triumph over the Tzar!-- were heavily censored, removing references to the starvation, death, and destruction ordinary citizens endured during this time.
For example, Cement (1925) is a novel written deliberately in the Soviet Realist style about how one lone Soviet hero tries to move the people of his town to really appreciate the cause of Communism and support the things which must be done. Even this novel was censored and republished with changes to its 1941 edition because a line refers to the depth of starvation ordinary people were enduring:
"Although we're poverty-stricken and are eating people on account of hunger, all the same we have Lenin."
So-- not only do you have to sing the song in the acceptable style about the acceptable subjects, but you have to make sure you don't have any rough edges that make the state look bad in any way. If you were a valued artist who produced something that didn't adhere to these ideas, your work would be censored or your previous works would be removed from circulation; you could also end up in prison. Stalinist censorship wasn't just in themes; it was also in the nature of truth itself. You've probably seen pictures where enemies of Stalin have actually been erased from history.
When Khrushchev came to power in 1953 he wanted to rule very differently than Stalin and consequently tried to liberalize censorship practices somewhat. Still: central publishers would censor and edit, removing anti-Soviet content and sometimes removing content that was pro-other countries, like France or the USA.
For a book to be published, it had to meet the Party standard. All publishing facilities were owned by government; all materials printed were reviewed and edited to meet standards of political belief. Agatha Christie could be available if it were not considered offensive and was pre-edited. (Actually, there was a 1987 Soviet adaptation of Christie's And Then There Were None, for instance.) But it would have been a very limited, truncated, edited selection.
Samizdat
Samizdat means "self-publishing." It mean taking a typewriter and typing up copies of banned material and circulating it underground-- typically political, but it could be lots of other things too, including literature and poetry. It was risky. In the typical black Soviet humour style:
"Samizdat: I write it myself, edit it myself, censor it myself, publish it myself, distribute it myself, and spend time in prison for it myself."
Samizdat was made difficult by the threat of prison time and the lack of availability of typewriters. Some people have claimed that each typewriter had unique manufacturing traits so KGB could hunt down dissenters by the way each character looked but my searching suggests this is probably just urban myth. Either way, in the mid-century USSR, there was limited access to limited materials, and those that were circulated through dissident networks tended to be political and brief, like leaflets.
Glasnost
From the Thaw until Gorbachev's rise to power and his transparency reforms of the mid-1980s, Soviets could expect to get more free access to movies and books than a generation earlier under Stalin, but state censorship was still very heavy. This is when you could more readily pick up foreign books from black market smugglers bringing cool stuff from Hungary (still Soviet but less heavily managed).
When Gorbachev brought in Glasnost, the culture of censorship lifted still further. Borders were also opened more, so that lessened capacity to prevent citizens from accessing materials undesired by the state.
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