In Japan, families used to gather for the New Year and spend few days together.
From the 28th of December until the 30th, families used to make Mochi (sort of rice cake) in family, and then install it in the housse as a gift to Gods.
They offer gift to gods in order ask them to protect the house for the coming year (fire, leak...). So they put sort of gift in diffrent rooms (kitchen, toilet, bathroom...).
Picture from : http://www.annakachie.com/blog/wp-content/uploads/2008/12/288.jpg
They let the mochi until around the 11th of January, and then have to eat it in family.
Under picture from : http://i3.sinaimg.cn/edu/2016/0203/U11035P42DT20160203102930.jpg
In the past, most of the shops were closed on the 1st, 2nd, 3rd of January, so families had to buy in advance ingredients and prepare meals for few days that they put in special boxes. This is now the New Year Meal, called "Osechi ryori" (おせち料理). Everything cooked in this box has a signification. Japanese people aslo eat Soba (noodles) at New Year, symbol of longevity.
Nowadays, shops are still open, so people continue to cook this New Year meal, or order it, but in smaller quantity. They usually don't finish everything at once, so keep some rest for next day.
On New Year, aldults give money to youngers. It is called "Otoshidama" (お年玉・おとしだま). Usually, children could receive it from grand-parents, brother/sisters, cousins, aunt/uncles, people close to the family that they meet at New Year.
In general they receive Otoshidama every year, until they finish school and began to work. So it depends of people, but they can receive it until Highschool, if they start working after highschool, as receive it until the end of the university... However, once they start to work, it is their turn to give "Otoshidama" to youngers.
Recently, Japanese people don't really gather every year for New Year. In fact when I have asked to my colleagues, they told me that the majority of people probably don't celebrate New Year anymore, especially when there are no young children at home.
Coming back to his hometown cost money, and takes time, especially at this period of the year. So nowadays, japanese people prefer to travel or to stay with their children for the New Year.