A popular greeting to bring in the new year, which is equivalent to “Happy New Year”, is 新年快乐 (Xīnnián kuàilè). I have often heard my Chinese friends say, 元旦快乐 (yuándàn kuàilè), which means the same thing.
Another popular greeting is 恭喜发财 (Gōngxǐ fācái), which translates are “Congratulations and be prosperous”. There is a very popular song that is played every new year almost everywhere you go. Listen to this song:
As a joke, some youth would say the phrase, 恭喜发财，红包拿来 (Gōngxǐ fācái, hóngbāo nálái). This phrase translated in English means, “Congratulations and be prosperous, give me a red envelope”.