At least some of what we know about crucifixion comes from the one historical person who we know was crucified and then placed in a tomb in Jerusalem.
The burial process is pretty well understood. If you had a tomb (if your family was wealthy enough to own one - or had been at some point in the past), you first took the body of the dead person into the tomb where they get placed on a stone table of sorts. The body is wrapped and embalmed. It gets left there for a year (or longer). After that time period, what is left is gathered up, and placed in a stone box (an ossuary). A typical ossuary could contain the remains of several people (entire families potentially) - you would simply add to the pile inside when someone died (or until it was full). For the poor, there was usually a double burial. First to get the decay for the corpse (and the burial was to protect the body from scavengers). Later it was dug up and moved to its final resting place (another burial in a cemetery).
You can see parts of this process is various well known (and sometimes contested) artifacts right? The Shroud of Turin (the burial shroud in theory used for Jesus). The much more recent ossuary with the inscription James the son of Joseph the brother of Jesus. And so on.
So, in 1968, at Giv‘at ha-Mivtar, an ossuary was found in a tomb that contained what was clearly a victim of Roman crucifixion. It remains (I think) the only such victim ever discovered in Israel. Part of the reason for this discovery had something to do with technical problems during the crucifixion. Normally, when the guy is dead, we would expect the nails to be removed (perhaps even reused) and the body taken down and disposed of. In this case, the pole was made of olive wood, and the nail for the feet hit a hard knot in the wood and bent around it (forming a bit of a hook). When they couldn't pull it free, they simply used an axe to chop off the guys feet (at the ankle) to remove the body, and then ripped the rest out of the pole (the feet, the the nail, and some of the wood attached to it were included with the rest of the body and eventually placed in the ossuary). There was evidence in this case for a plaque (of the sort described in the gospels) made of a different kind of wood than the olive wood from the pole.
What also comes out of this is the problem of preservation. The ossuaries at this site had a moisture problem. All of the ossuaries at this tomb were about 30% filled with a thick liquid - containing a lot of limestone (much of it coming from the ossuary itself). This limestone liquid did a great deal to help preserve the bones at the bottom of the ossuary - and while it made it difficult to really figure out initially what was going on with this guys feet (his name was Yehohanan) it actually helped preserve the bone structure and keep the nail intact under a coating of limestone buildup. So while the remains were fragile, they hadn't come apart, the nail hadn't come out, and so on. This allowed us to see the way in which they were all put together during the crucifixion.
In all of this, we have several additional ideas. Crucifixion was generally reserved for slaves and political criminals. The process (for the Romans at least) is well documented. And while the process of disposing of bodies probably was generally quite simple, in cases where the family could afford a tomb and to go through the process of burial in this way, it seems likely that the Romans would allow them to do so. Since most of those crucified were not wealthy, that at least in part explains the scarcity of remains. The others, if not claimed, would normally have been taken to a dumping site and left there (not simply left in the streets) although scavengers would've course take care of exposed remains.
However, Jewish law generally required burial (part of the question in the OP). And this is where we get information from the Mishnah (Talmud).
The most vocal about this is the Talmudic work titled Sanhedrin (which has the rules for capital punishment), but it comes in both the Jerusalem and Babylonian Talmudic versions, and with a Tosefta to accompany the Mishnah. So here is an excerpt from the Babylonian Sanhedrin Mishnah:
And then they undo him immediately. If he stayed there overnight, violates a negative commandment on his account, as it says, (Deuteronomy 21:23), "His body shall not remain all night upon the tree, but thou shalt surely bury him the same day; for he that is hanged is a reproach unto God...." That is to say: why has he been hanged? Because he 'blessed' God, and God's name has become desecrated.
Said Rabbi Meir, when a human being is in distress, what expression does the Divine Presence use, as it were? "My head is in pain, My arm is in pain." If so, the Omnipresent feels distress over the blood of the wicked that is spilled; how much more so over the blood of the righteous. And furthermore, anyone who leaves a dead body hanging overnight transgresses a negative commandment. But if one leaves a body hanging overnight for the sake of its honor, to bring it a coffin or shroud, he does not transgress. And such a body would not be buried in the grave of his ancestors. Rather, two grave-sites were set for the courthouse, one for those put to death by decapitation and strangulation, and one for those put to death by stoning and burning.
When the flesh decomposed, they collect the bones and bury them in their proper place. And the relatives come and greet the judges and the witnesses, as if to say, we hold nothing against you, since your verdict was just. And they would not mourn, but they would grieve, since grief is only in the heart.
As far as a guard being placed, there isn't any way to verify this. Stones at the entrance to these family tombs is something we know from archaeology as a common practice (to keep scavengers out). Now obviously, crucifixion isn't one of the proscribed punishments in Jewish law, and so there is some leeway in how they could deal with these bodies (there wasn't a separate cemetery for crucifixion victims), and so we don't really know how this was usually handled in Jerusalem under Roman occupation. We only have a minimal amount of evidence. But from what we have, the circumstances with Jesus would have been unusual, but not outside of what we might expect.
Of course, the Roman occupation of Jerusalem continues for a significant period of time. And the narrative about Jesus would (if it were fictional) be more of a contemporary fiction rather than a historical fiction. And so we don't really expect to have issues here in these circumstances. We have more skepticism when the narrative details are intertwined with proof-texting - since this tends to come up as we get interpretations of the movement and the shift towards a more institutional church (when the narratives are re-interpreted to create some of the prooftexting that we see).
Mark, for example, contains a number of details about the crucifixion which match reasonably well to our expectations based on independent information. The part that might grab our attention would be something like Mark 15:28 - "And the scripture was fulfilled, which saith, And he was numbered with the transgressors." This is where we start getting significant interpretive layering in the text (and potential editorial insertions). Jewish tradition in the Mishnah that I quote above deals with hanging on a tree - and so when we get the next layer of traditions in Acts, we see that this has already become a part of the interpretation:
Acts 5:30 The God of our fathers raised up Jesus, whom ye slew and hanged on a tree.
Acts 13:29 And when they had fulfilled all that was written of him, they took him down from the tree, and laid him in a sepulchre.
Acts 10:39 And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree:
You can see how this shows an interpretive layer being applied on top of the crucifixion narrative - and being done in a specific way to connect it back to earlier texts (suggesting why the Jews might have killed Jesus - since it was only for certain issues that you might be hung from a tree, and so on). This doesn't make the crucifixion fictional - but it illustrates that we have a developing formal understanding of the earlier narratives within Christianity as it transitions out of the early movement and into an institution. And that these understandings also change the way that the early Church is talking about the crucifixion. And (in my personal opinion) this helps us conclude that the original crucifixion narratives were part of the earlier traditions about Jesus - and so more likely to reflect a historical reality. (And his is partly why the figure of a political revolutionary is popular among the various historical Jesus models).
Ben McGuire