Actually, New Years' Day (Shougatsu) in Japan has only been celebrated on Jan. 1st of the Gregorian calendar since the Meiji era. Five years after the Meiji Restoration, the Japanese adapted the Western calendar, probably in order to smooth relations with outsider countries (ahem, Americans). Previous to that time, they used the Lunar calendar. This year the Lunar New Year falls on Jan. 23rd, but since people no longer celebrate it on this day in Japan, January 1st it is!
Shougatsu is the day after celebrating the corporate festival that is the Christmas holiday + post-holiday cleaning where people rush around making shrine visits and trying to get their New Years' cards and omiyage to the right places and people on time. Post offices even guarantee the arrival of these items on Jan. 1st, if you send them out in a certain time frame and label them 'nengajou'. Friends, family members, and work places or helpful people are all the usual recipients of these sorts of gifts. Most people buy the postcards pre-printed with that years' zodiac animal, a New Years' message of traditional sayings or haiku celebrating firsts of the year, or can get them printed at home or at department stores with favourite designs, but some choose to buy blank ones and write/draw them by hand for each person. It's very important to continue good social relations and pay off any remaining debts before the new year begins in order to have a fresh start!
There is an exception to the sending of New Years' Cards: when there has been a death in the family, a household member will send out a postcard called 'mochyuu hagaki' to inform friends and relatives of the death. This also signals them to not send New Years' cards, as it is considered disrespectful to the person who died.
Special foods called 'osechi' are eaten on this day, too! Mostly, the traditional foods are sour, salty, or dried. Remember that refrigerators are only a recent invention, and with all of the preparations to be made for perhaps the biggest holiday of the year, there was little time or energy left over for cooking- and no restaurant would be open that day, either! Konbu (seasoned seaweed), kamaboko (a kind of fish cake), and ozouni (zoni, a soup made with mochi and dried vegetables and fish), along with special bean dishes are eaten during this season.
Some people make shrine visits on the night of Dec. 31st (so that they can be there as the year turns) or on Jan. 1st. Most people no longer wear kimono that day, but everyone dresses their best! The first shrine visit of the year, regardless of a persons' religions or lack thereof, is a traditionally important visit called 'Hatsumoude'. Buddhist temples will ring special bells 108 times on Midnight of Dec. 31st to symbolize the 108 sins of humanity, and the 108 worldly desires of man. Ringing these bells is said to wash away sins of the previous year, and to give way to a new beginning.
This year is the year of the Dragon! I can't wait to wear my dragon obi to celebrate! <3