At the time of Jesus, there were two popular modes of burial.
The method more popular with the poorer classes, which of course in those days meant most people (and some groups such as the Qumran community) was burial on the ground. It involved burying the body of the deceased (sometimes placed in a wooden coffin) in a trench grave, not unlike modern day grave cuts. After the pit was filled in, the grave was marked either by erecting a headstone or a pile of rocks at one or both ends, or simply pouring a mixture of lime/chalk and water over the backfill, so that people would recognize the presence of a grave and avoid accidentally passing through it and becoming ritually impure as a result.
Archaeologists have not found many examples of this type of burial given the inconspicuous and highly flimsy nature of this type of grave; in other words, it’s easy to miss and more susceptible to destruction and decomposition. Other similar field burials are cist graves (where you dig a pit and line it with things like wood planks or stone as walling) and shaft graves (five-to seven-meter trenches - more deeper than a cist grave - with a niche at the bottom for the body or the coffin to be placed in).
The cemetery at Qumran. As you might see, not really much of a sight - just piles of rocks serving as grave markers. At the time of Jesus, many people (those who could not afford to commission or buy a ‘cave’-type tomb) would have been buried like this. One of the things that makes the Qumran burials so striking (the graves here show a number of differences from graves in other areas) is that skeletal analysis indicates the people buried in there to be from relatively high social classes: did these men deliberately choose to be buried like the common poor – ‘six feet under’ on the ground? (There were many natural caves around Qumran, but none are used for burial. Note that these graves were actually carefully arranged - these weren’t just rudimentary, crude pits used for hasty burials.)
Since Jesus wasn’t really from a wealthy family, had He lived a normal sort of life there’s a chance that He would have been buried in this sort of earthen grave - if His family did not already own a sort of family tomb. In fact, had Joseph of Arimathea not stepped in, it would have been likely that He would have still been buried ‘six feet under’ after His crucifixion. But since Jesus died in the late afternoon, the lack of time before Sabbath began (the Jewish day began at sundown) meant that there was not enough time to even dig a pit grave for Him. (It is true that in some cases crucifixion victims were denied burial, but we know from sources like Josephus that in Palestine those who died by crucifixion are allowed to be buried, if because of the stipulation on Deuteronomy 21 that condemned men who were stoned to death and whose bodies are hung on a tree must be taken down and buried on the same day - by the time of Jesus this passage was interpreted to include crucifixion victims, those who were hung on a ‘tree’ to die.)