(By the way, I suggest more specific titles for a question, since that's all some people see in the discussion list. "Nazi Germany question" is way too wide open.)

TL;DR: as things got worse at Stalingrad, news of the east and of Stalingrad were more and more suppressed. The surrender was trumpeted as a defeat down to the last bullet, with 3 days of mourning and spin as being heroic self-sacrifice, but after that, it was mentioned less and less until it was suppressed.

This is covered by Jay W. Baird, "The Myth of Stalingrad", Journal of Contemporary History, Vol. 4, No. 3, Urbanism (Jul., 1969), pp. 187-204, http://www.jstor.org/stable/259739 . Unlike some other tertiary sources I found, he at least provides citations, sometimes to primary sources.

Goebbels did suppress some information leading up to it: for example, 24 November 1942 they mentioned a breakthrough, but not encirclement.

Baird wrote, "There is little question that this admission was forced on Hitler by the Soviet Union's own Special Announcement, which was made public on 23 November". I wondered why a totalitarian government worried about foreign announcements, but later the article says that many Germans listened to Radio Moscow; for one thing, at intervals they listed names of POWs. He also wrote that "The enemy tactics included postcards and letters to persons in Germany whose relatives had been killed in action or taken prisoner on the eastern front. Bona fide letters were interspersed with fraudulent ones.", but I have no idea how, because neither side observed the Geneva Conventions.

News of Stalingrad and of the East (German armies being pushed back) were more and more suppressed over the next two months until the fall.

Goebbels and Hitler met for more than 8 hours on 13 January 1943 (a couple of weeks before the end at Stalingrad) to talk about the general approaches to be used in propaganda in the future. The news was to be gradually broken to Germany.

"On 16 January the OKW admitted for the first time that for weeks the German troops at Stalingrad had been engaged in a defensive battle against an enemy who was 'attacking from all sides'." Reports on each of several future days talked about the heroic resistance and self-sacrifice by the German troops. By 30 January, the day before Paulus's surrender, "Hitler and Goebbels realized that the propaganda coverage of the disaster had to be treated in an extraordinary fashion. Neither factual reporting nor traditional misrepresentation would serve their purpose, and they decided that the sacrifice along the Volga could be explained only by way of a myth. Reality was thus to be reinterpreted."

On 3 February the press was informed that the announcement was going to be made, and "In several days of mourning the German people will honour their brave sons, men who did their duty to the last breath and to the last bullet, and as a result have broken the back of the Bolshevik assault on our Eastern front." The spin was to be a heroic epic, "stirring", "outshines every feat of heroism known to history", "this ultimate, self-sacrificing dedication to Germany's final victory, will blaze forth like a sacred flame", and such.

I've seen different reports of how it was announced, but this account looks authoritative. This article says

The radio broadcast of the Special Announcement opened with solemn marches, followed by drum rolls and three stanzas of one of the saddest of all German war songs, "Ich hatt' einen Kameraden". Then came the announcement of the fall of Stalingrad, followed by the playing of the German, Italian, and Croat national anthems. [footnote: citing Ernst Kris and Hans Speier, German Radio Propaganda: Report on Home Broadcasts during the War (London, 1944), 431-2.] Three minutes of silence were followed by Beethoven's Fifth Symphony, and a three-day period of mourning was ordered. The entire schedule of programmes was changed for several days to fit the Stalingrad propaganda line. [footnote: citing Hinkel to Goebbels, and "Beethoven's 'Eroica' was included in many broadcasts."]

The OKW announcement said that the army had been "true to their oath" and said that their sacrifice had been essential to have tied down major forces, and enabled counter-measures that would ensure success of the campaign. But Hitler realized that it could cause a crisis in morale, so he ordered that February that military commentaries be discontinued, and later that no references be made to it. E.g., when Tunisia was being lost, the press was directed that "in no circumstances" was there to be any comparison to Stalingrad. The details of Stalingrad were never published, and they tried to confiscate all letters from the front before delivery. (45 out of 1900 made it thru anyway.) But rumors got out anyway, saying that 90,000 prisoners had been taken (which wasn't far off) rather than all of them fighting to the last bullet as had been stated.

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A side note: that just says that there was "three days of mourning". A bootleg book of some sort had "all theatres and cinemas were ordered to close", but I don't have a citation.

Some books state that Bruckner's Seventh Symphony was played before the announcement. John Keegan even wrote (The Second World War and Six Armies in Normandy) that German radio played nothing but that for three days, or nothing but that and Beethoven's "Eroica" symphony, respectively.

Gilles Houle, "The Adagio of Bruckner's 7th: The beginning of the end for the Nazis", https://www.abruckner.com/Data/documents/Houle_Goring_and_Bruckner.pdf , looks interesting, but he gives only one citation. He states that Göring was to give a speech live at 11 AM on 30 January to commemorate the 10th anniversary of the Nazis taking power, but a British raid knocked the radio headquarters off the air for an hour, and "During the interruption, the authorities decided to play, as an interlude, Furtwängler's recording of the « Adagio » of Bruckner's 7th Symphony." Maybe that was a source of confusion? BTW, the one citation was to the publication of Göring's 3 February speech announcing the defeat.