Romans had various gods and traditions that they followed closely. From our modern point of view we might take many of their beliefs as superstitious or irrational, but we must keep in mind that they lived in another time and era and tried to make sense of life using omens as their guide.
When it comes to funerals, they had specific procedures that they followed closely. When someone was on the verge of death, the family and relatives would watch over the dying person. When the final hour struck, the closest relative would try to catch the last breath with a kiss and close the dead person's eyes.
Then the dead man's name was called out loudly, a practiced called conclamatio. That must be a frightening experience really. All is quiet, the dying man has passed away; his soul is slowly leaving the body, still numb and in a daze and in great confusion, and all of a sudden somebody shouts his name a couple of times!
After that a small silver coin, obolus, was placed under the tongue or on the eyes of the deceased, which was intended as payment for the skinny and cranky ferryman Charon in Hades. Charon was responsible to take the soul of the dead person across one of the five rivers, the Styx being the most famous one, into the underworld and the coin, along with proper burial or cremation, was to ensure he would be able to pay his fare down that dark river. Yet Charon was a moody and unreliable fellow and often he could not even be trusted; when you are looking the other way or enjoying the after-world scenery, he could push you into the river for no apparent reason.
After death, the corpse would be washed and anointed with oil and perfumes, which was usually done either by slaves or by undertakers. Then the body would be dressed in the person's best clothes and displayed in the atrium for all to come and mourn.
Funerals had started as a nocturnal tradition, but later richer Romans preferred the day, so that they could give sumptuous funerals to impress others and display both the riches and the popularity of the person in question. The poorer people who could not afford elaborate and costly rites usually held their funerals at night, in secret, where nobody could see them and their lack of display went by unnoticed.
The funeral was usually held on the ninth day after death and was headed by musicians. In memory of the deceased often theater actors and buffoons were hired to represent the character and personality of the deceased by imitating his words and actions in his memory. So much for speaking well of the departed. Sometimes women, called praeficae, were hired to wail and cry in grief; these were so-called professional wailers who had their own calling cards for funeral services.
Female relatives and friends would usually mourn and lament in loud wailing voices, beat their breast and tear their hair. Men were mourning too, but were careful not to show their feelings and control emotional outbursts, since a public display of emotion was considered effeminate. Romans were quite "macho" in this respect.
The deceased would be carried along in a coffin or a stretcher, and the last rites would be performed outside of the city, where the body would be either buried or cremated along with objects that belonged to him, that he held dear and that he could possibly need in the afterlife. Not only his teddy bear, but also objects like combs and gel so he could still look good and spiffy in the afterlife.
While cremations became more common in later Roman times, especially during the Republic, the poor continued with burials. Burials became a more common and widespread practice after the growing influence of Christianity. Yet Christianity had a different perspective of how funerals should be held and barred buffoons and professional wailers from this ceremony; in other words, dying became a dead serious matter.