A bit of a disclaimer before I begin: I am a student of Literary Chinese, not of Chinese History, so my understanding of these sources comes from a more literary rather than historiographical angle. However, as The Record of the Grand Historian (Shiji) is considered a seminal work in both the literary and historical fields, I have a reasonable amount of familiarity with the source work of which you speak.

The passage regarding the killing of the surrendered Qin troops comes from Scroll 7 of the Shiji, which is primarily a biography of Xiang Yu.

In it, Sima Qian writes: Xiang Yu summoned his generals Ying Bu and Pu and strategized with them. He said, ‘The (surrendered) Qin soldiers are numerous, and their spirits have yet to be quelled. If we reach the Central Plain and they refuse to listen to our commands, the situation will turn dangerous. Let us instead slay them, and enter the territory Qin alone with (the captured former Qin commanders).’ And so the soldiers of Chu struck at night and dishonourably killed 200,000 or more of the Qin soldiers by the south of Xin An city.”

You’ll notice that my translation makes no mention of the Qin soldiers being buried alive, and that is because I believe that particular anecdote is in fact a mistranslation of the italicized section above. The issue stems from the character in question that Sima Qian uses – “阬", which can mean both “to bury”, as well as “to kill dishonourably”. As is often the case in Literary Chinese texts, Sima Qian does not clarify which meaning he intends to use here, so we have to try and deduce it on our own.

The first question we should ask is whether it is feasible to bury 200,000 troops alive, and as you might expect, the answer is “definitely not”. From the passage above, we know that Xiang Yu was worried about the possibility of a rebellion amongst his captured Qin soldiers, so we have to presume that they posed a significant military threat to him and his men. Given this, why would he choose such a time consuming and difficult form of execution? Instead, it seems far more likely that he killed them in a dishonourable surprise attack.

The second question we have to look at is how Sima Qian uses the character 阬 in other places of the text. Another prominent use of the character comes in the biography of Bai Qi, a famous Qin general who reputedly killed 400,000 prisoners after the battle of Changping. Burying 400,000 men alive seems even less feasible than burying 200,000, suggesting that Bai Qi killed them dishonourably rather than specifically by burying. In fact, Sima Qian writes that on his deathbed Bai Qi remained haunted by his decision to 阬 those prisoners of war. Given that burying alive was not a particularly uncommon form of punishment/funeral rite while breaking a promise to a defeated enemy was considered a great sin, it seems more likely that the dishonourable reading was the one Sima Qian intended.

Finally, archaeological evidence from the Changping gravesite shows many of the soldiers there had perished from arrow/sword wounds rather than suffocation. This lends credence to the theory they were killed first, rather than buried alive.

I am happy to cite more textual evidence from Sima Qian and his near contemporaries but as I am mostly familiar with primary sources the other examples might a little inaccessible to those unfamiliar with Literary Chinese. I am also willing to provide proof of my Literary Chinese credentials if this is required by the rules of the subreddit.

As /u/lordtiandao said, the scope and scale of such events was unusual even at the time. That said, the idea of funerary vivisepulture was pretty common during the Qin and prior. Tombs in places like Fengyang, Anhui have been unearth with signs of several and sometimes even a dozen or more people having been entombed alive with the deceased, along with trinkets, religious and ceremonial objects, and currency. But probably the most (in)famous case was the First Qin Emperor, himself, who seemed to have been rather taken with the idea of burying people alive. There's the "Burning of Books and Burial of Scholars" incident in which Sima Qian writes:

The first emperor therefore directed the imperial censor to investigate the scholars one by one. The scholars accused each other, and so the emperor personally determined their fate. More than 460 of them were buried alive at Xianyang, and the event is announced to all under heaven for warning followers. More people were internally exiled to border regions.

And then there's the issue of the emperor's ironic death and entombment within his necropolis outside Xi'an. Once again Sima Qian relates it:

The Second Emperor said: "It would be inappropriate for the concubines of the late emperor who have no sons to be out free", ordered that they should accompany the dead, and a great many died. After the burial, it was suggested that it would be a serious breach if the craftsmen who constructed the mechanical devices and knew of its treasures were to divulge those secrets. Therefore after the funeral ceremonies had completed and the treasures hidden away, the inner passageway was blocked, and the outer gate lowered, immediately trapping all the workers and craftsmen inside. None could escape.

Now... as to how accurate and trustworthy such accounts are? Hard to say for sure... but Sima Qian has been pretty widely criticized by more modern historians for playing kinda... fast and loose with specifics (especially numbers... he's terrible at numbers... that whole 200,000 soldiers bit, take it with a sizable grain of salt. Throughout ancient Chinese literature, numbers were used far more for effect than accuracy... Sima saying multiple hundreds of thousands is probably more akin to me saying "a gazillion soldiers got killed" than any reflection on the actual numbers.) Likewise with the burying of the scholars and the mausoleum entombment... since all there really is one guy to draw from, writing a century or more after the events he was chronicling, and with a clear narrative bias in terms of the fact that he was writing for the succeeding dynastic government... you have to wonder how "fair" his portrayal of Qin Shihuang and his actions may have actually been.

As far as I know, the only other instance when surrendering soldiers were buried en masse was the Battle of Changping in 260 BCE. As for how it's done, I'm afraid there doesn't seem to have any detailed records.