Do's:

Wish everyone you meet a happy New Year by saying
'gong xi fa cai', which translates to: 'Have a happy and
prosperous New Year!'
Wear articles of red clothing because red symbolizes luck.
Eat vegetarian food because it's not good to see blood.
Buy new trousers because the Chinese word for trousers
is 'fu', (Chinese homonym for wealth)
Children should stay up as late as possible on New Year's Eve for it is believed that the later they stay up, the longer their parents will live.
Visit family (especially those older than yourself) and friends to pass on your wishes on good fortune for the New Year. (plus kids and single people will receive lai-see lucky red packets full of money.
Give two lai see to each child. Because happiness comes in two's, do not just give one. This is your way of passing good luck to the next generation. Business owners also give lai see to employees and associates.

Don'ts:
Don't wear white or black clothing, since they are the traditional colours of mourning.
Don't buy new shoes for the first months of the New Year, because the sound of shoe in Chinese is 'hai'. 'Hai' is similar to the sound of sighing, which Chinese believe is not a good way to start the year.
Don't wash your hair for the first three days of the New Year, because the Chinese word for hair is a homonym for the Chinese word for wealth. Therefore, Chinese believe it isn't a good thing to 'wash away your wealth' right at the start of the New Year.
Floors may not be swept and garbage may not be disposed of on the first day of the New Year for fear of casting riches out the door.
Don't swear or quarrel.
Don't break any dishes, otherwise you may incur more misfortune for the New Year. In the event of breaking a dish, quickly say 'Peace for all time', and the bad luck will be warded away.
Don't greet people who are in mourning.
Don't drop your chopsticks.
Don't say the number 'four' (Chinese homonym for death) or mention death.
Don't borrow or lend money.