I identify it as a sort of Christmas celebration. How did I even decorate?
If you were a Senator or a member of the Equitēs, Rome's business middle class, you would go down to the forum on the 17th of December wearing your formal toga and congregate with the others at the base of the Temple of Saturn. There the priests would perform a very large sacrifice, and then would follow a large barbecue banquet. This had been the custom since at least the late 2nd century BCE. While the ceremony itself was for the elite, anybody could join in the banquet on the street, and there were probably normally people filling the forum and spilling out into the adjoining spaces, much like New Years Eve in Times Square now. We hear that it was a time of general merry-making for all involved, and all the businesses and official goings-on were shut for the occasion. While this convivium publicum was going on, thousands more were back at home enjoying a similar party atmosphere. It is likely that the public barbecue banquet of the forum was mirrored in streets all over the city, perhaps fueled by less grand sacrifices to Saturn or other gods in those places (we don't know). And the party extended into private homes, as well, again much like New Years Eve. Drinking and gabling were both common, as were the shouts of the revelers, including a seasonal cry of "Io Saturnalia!" We also hear that revelers wore little hats of a certain type (pilei), though no one knows exactly what they were, or why. It is likely not even the Romans knew for sure. Pliny the Younger so hated all the noise of Saturnalia that he says he preferred to retire to his inner chambers to avoid being a party-pooper and also to escape the noise (so see his letter 2.17).
The general theme of the event is having fun, blowing off steam, and relaxing the boundaries of class and decorum. Some suspect that in very ancient times, agricultural workers from the hinterlands came into the city and rubbed shoulders with their more urbane fellows at the sacrifice and banquet, and that from that a feeling of unusual camaraderie developed. Famously, by the time of the Late Republic, a tradition had come about wherein slaves were "served" by their masters at the festivities. Regardless of what exactly this meant, we can be sure there was an atmosphere of relaxing or ignoring the rigidities of social boundaries during this event. It has been argued that Saturn is connected to fertility rites from the most ancient times, and also with transitions between seasons and across liminal spaces (field to city, planting to harvest, fire, etc). It is here also that little gifts were exchanged, typically small symbolic ceramic objects (sigillaria) or candles (cerei), from which developed the familiar custom of Christmas gift-giving later.
By the Late Republic, Saturnalia lasted for seven days, beginning with this big party on the 17th of December. During the Empire, it varied from 3 to 7 days. We don't know what went on exactly on the other days, but the main "religious" component was the sacrifice on the 17th and the ensuring barbecue. As usual, the best sources will be Dumezil Archaic Roman Religion and Scullard Festivals and Ceremonies of the Roman Republic, but they, like here, have a lot of "we don't know" for Saturn. Unfortunately for us, a few very late sources, from the Christian end of the late Empire, write about the Saturnalia and hopelessly muddle it for us. As far as the true nature of this holiday and its shadowy origins, these sources do more harm than good. Also, because this is among the most famous Roman holidays, the modern internet is stuffed with misinformation on it. Searchers beware.