Chinese New Year - 新年

How to say Chinese New Year in Mandarin?

春节 chūnjié 'Spring Festival' (used in China)

新年 xīnnián 'New Year'

农历新年 nónglì xīnnián 'Lunar New Year' (because it follows Lunar calendar)

How do you say/congratulate Happy New Year?
恭喜！恭喜！gōngxǐ gōngxǐ '(respectfully) wish (you) happiness'
恭喜发财！gōngxǐ fācái 'Wish happiness and prosperity'
新年好！xīnnián hǎo 'New Year Good'
新年快乐！xīnnián kuàile ' New Year Happy'

What can you wish people?祝你。。。zhūnǐ (wish you)... ＋
        身体健康 shēntǐ jiànkāng 'Good health'
        万事如意 wànshì rúyì 'Everything as you wish'        

Married People or Senior people will give 红包 hóngbāo (Red Envelope containing cash) as a symbol of luck to unmarried people, kids or lower-ranking people (like employers to employees).

Here is a popular song called Gongxi Gongxi with Pinyin that you will hear in every Chinese community during Chinese New Year:

Learn more:
http://laowaichinese.net/text-message-greetings-for-chinese-new-year.htm
http://mandarin.about.com/od/chineseculture/a/newyear.htm

Song: 月亮代表我的心

Many foreigners (laowai: 老外) learn Chinese without knowing a single Chinese song, not the slightest interest in pop culture - Well, Chinese pop culture isn't exactly the same as Westerns, but still I think this is the evergreen song that learners should know (like Beatle's).

月亮代表我的心 yuè liàng dài biǎo wǒ de xīn

你问我爱你有多深
我爱你有几分
我的情也真
我的爱也真
月亮代表我的心

你问我爱你有多深
我爱你有几分
我的情不移
我的爱不变
月亮代表我的心

轻轻的一个吻
已经打动我的心
深深的一段情
教我思念到如今

你问我爱你有多深
我爱你有几分
你去想一想
你去看一看
月亮代表我的心

轻轻的一个吻
已经打动我的心
深深的一段情
教我思念到如今

你问我爱你有多深
我爱你有几分
你去想一想
你去看一看
月亮代表我的心
你去想一想
你去看一看
月亮代表我的心
   
nǐ wèn wǒ ài nǐ yǒu duō shēn
wǒ ài nǐ yǒu jǐ fēn
wǒ de qíng yě zhēn
wǒ de ài yě zhēn
yuè liàng dài biǎo wǒ de xīn

nǐ wèn wǒ ài nǐ yǒu duō shēn
wǒ ài nǐ yǒu jǐ fēn
wǒ de qíng bù yí
wǒ de ài bù biàn
yuè liàng dài biǎo wǒ de xīn

qīng qīng de yī gè wěn
yǐ jīng dǎ dòng wǒ de xīn
shēn shēn de yī duàn qíng
jiào wǒ sī niàn dào rú jīn

nǐ wèn wǒ ài nǐ yǒu duō shēn
wǒ ài nǐ yǒu jǐ fēn
nǐ qù xiǎng yī xiǎng
nǐ qù kàn yī kàn
yuè liàng dài biǎo wǒ de xīn

qīng qīng de yī gè wěn
yǐ jīng dǎ dòng wǒ de xīn
shēn shēn de yī duàn qíng
jiào wǒ sī niàn dào rú jīn

nǐ wèn wǒ ài nǐ yǒu duō shēn
wǒ ài nǐ yǒu jǐ fēn
nǐ qù xiǎng yī xiǎng
nǐ qù kàn yī kàn
yuè liàng dài biǎo wǒ de xīn
nǐ qù xiǎng yī xiǎng
nǐ qù kàn yī kàn
yuè liàng dài biǎo wǒ de xīn