Romans would have sacrificed liberally to the Gods before and after his deification in September, directly to Augustus himself. This is commonly called the Imperial cult and came to be early in Augustus' reign and continued long after his death.

Common sacrifices were wine, barley and animals. Sacrificed barley would be burned, as might some token bits of the animal like a patch of hair or feathers. Sacrificed animals would be butchered, with certain bits designated for the Gods and the other cuts going to a feast. It was thought that the Gods enjoyed the smoke, so burning sacrificial bits and cooking the meat were additions, not detractions from the ritual.

Another interesting thing was that anyone could sacrifice. You needed no license from the state nor any spiritual authority to do so. Even slaves could and did sacrifice. Public ceremonies with sacrifices were often sponsored by the state (moreso during Imperial times) or by prominent individuals for major events or holidays. Such public displays were lavish, with elaborate dress for the sacrifices, hymns and prayers, music and, invariably in my readings, a feast. A particularly huge feast, celebrating Caesar's relative Julia and Caesar's triumph, is described by Goldsworthy, page 470 (22,000 tables... maybe).

As to the funeral itself, which we know little about, it appears to have terribly portentous and somber. After passing, the body would be brought through the city to the family mausoleum by the deceased's family. The mausoleum would always be outside the city's nominal boundary. Masks of the family's ancestors would be worn to make it seem as if the deceased were being brought to the afterlife by his ancestors. Actors and musicians would also be hired for the procession. An example of this appears in Goldsworthy's Caesar (page 98). Cremation was the preferred burial mode for the time period, so the body would be burned on the site and then placed in a proper urn in its designated place next to the rest of the family. Mourning was common, though I'm not sure about male crying. Loved ones, clients and other mourners might tear their clothes or cry to express their anger or sadness. Nine days after the burial, the aforementioned feast would take place, accompanied by more sacrifices.

Keep in mind these were all terribly expensive and sometimes unwelcome displays. Only rich families could afford all the bells and whistles. They could stir up unrest if they were too lavish or piss off rival clans if they were purposely over the top, so many regulations evolved in the Imperial period to reign them in.