It is my understanding that in 46 B.C.E Julius Caesar made January 1st the New Year. If I was a Roman Citizen, how would I be celebrating the first Modern New Year.

Actually, January 1st was established as the New Year by the Roman Senate in 153 BC. The reason was actually for practicality. Before, the Civil and Consular year began on March 15, the Ides of March, as March was traditionally the first season in which Soldiers could muster for a fighting season. Once Spring began, there would be a few weeks for Roman citizens, who at the time were overwhelmingly farmers, to plant their crops, then head off to war, whilst their younger sons, wives, daughters, and slaves would maintain their properties.

This changed in 153 BC, where a military uprising in the Roman Province of Hispania (eastern Spain, near Catalonia), prompted a Roman response. However, when troops began to muster on March 15, they also had to board transports, sail across the Mediterranean, or March overland through the Alps, Southern Gaul, and the Pyrenees, and wouldn't arrive until July or August, which was towards the end of the fighting season.This problem was resolved by a decree of the Senate that moved the start of the Consular year from March 15 to January 1, which awkwardly placed it in the middle of Winter.

Thus, January 1st would largely be a political-religious holiday, with the two new consuls being sworn in, similar to inauguration day in the United States. Auguries would be taken, and public oaths of loyalty to the Republic would be sworn. The Roman calendar, which was based around ancient Roman agrarian practices, generally frowned upon harvesting or doing strenuous labor until the 13 of January. This time would largely be taken to to conduct personal auguries and rituals to attempt to divine individual fortunes in the New Year, so there were practical and religious considerations to be taken into account.

Additionally, there was a moveable feast, known as compitalia, that was dedicated to the Gods of the crossroads and the Goddess of the underworld. The festival apparently predates the founding of Rome and the Republic, and was instituted by one of the earlier Etruscan kings. The exact celebration would have ritual celebrations occurring at every crossroad in the city, with offerings given to the goddess of the underworld.

Each home would have small wool dolls of each member of the family hung around the doorway (similar to Passover), but with the expectation that the Gods of the Underworld would be contended with these as surrogates for those of the family. Additionally, heads of garlic would be offered, according to a tradition set down by Brutus after he overthrew the Roman King Tarquinius. According to legend, the oracles of Rome revealed that in order to spare each family, "heads would be sacrificed for heads," implying the heads of children sacrificed for the family. However, Brutus exploited a loophole, because the head of garlic and poppies is the same as that of the actual anatomical part of the body. So as tradition, Romans made these offerings.

Additionally, there was the festival of Sementivae, which occurred later in the month, near January 24-25, and was devoted towards Ceres, the goddess of agriculture, with the hope that there would be a good growing season that year.