Near the beginning of his poem "Fasti", Ovid has a kind of question and answer session with Janus about the meaning of certain new year traditions. We can use this to help us prepare for a Roman New Year.
Q: Why aren't the courts closed on New Years Day?
A: We make a token start of all business on the first day to make a good omen that we will be engaged all year.
Q: Even when I address other gods, why do I offer wine and incense to you first, Janus?
A: I am the guardian of thresholds. Through me you can have access to whichever god you please.
Q: Why are joyful words spoken on the Kalends, and why do we give and receive good wishes?
A: Omens attend upon beginnings. When the temples and ears of the gods are open, the tongue speaks no idle prayer, words have weight.
Q: What do the gifts of dates and dried figs mean, and the honey glistening in a snow-white jar?
A: For the omen, so that events match the savour, so the course of the year might be sweet as its start.
So here we have some fine traditions that we can follow now:
Clean your lararium on New Year's Eve, so that it is ready for the new year. Decorate it with flowers.
Make offerings to your Lares and to Juno, but first to Janus.
Whatever you do, make a token start of it on New Year's Day. Students take up a book and read for a few moments. Carpenters tap a nail. Whatever you do, resolve to have a prosperous year, with the help of the immortal gods.
Guard your words, offer good wishes and prosperity to all. Avoid dire words.
Give gifts of sweet dried fruits and honey, or other similar sweets, such as honey dipped cookies.