'Happy new year' can be translated to several ways in Chinese:
新年快乐-- xīn nián kuài lè
新年好 - xīn nián hǎo
恭贺新禧 - gōng hè xīn xǐ (this is often used in the writing)

New year is normally translated as 新年 (xīn nián).
新 (xīn) means new, 年 (nián) means year
快乐 (kuài lè) means happy