Don't greet a Chinese with 'How are you? nihaoma? 你好吗？'

Listen, you sound just like a foreigner when you say 'Nihaoma? 你好吗?'. Teachers like me feel obliged to answer: 'Wo hen hao, xiexie, ni ne? 我很好，谢谢，你呢?' - This conventional response sounds like those we learnt in any European language class including English - 'How are you' - 'I am fine, thanks. And you?'.
The common informal greetings can consist of two parts:

PART 1 - interjection of greeting

1. 嘿 hēi - hey
2. 嗨 hāi - hi
3. 喂wèi - hey; commonly used in telephone with an rising tone wéi
4. 诶 ēi - hey (when you bump into a friend; or when you're calling a friend who doesn't see you passing-by)
5. the above + optional 你好 or/and addressing the name

PART 2 - greeting question
1. Have you eaten?
(nǐ) chīfan le ma? (你)吃饭了吗?
(nǐ) chīle ma? (你)吃了吗?
(nǐ) chīguò le ma? (你)吃过了吗?
optional nǐ

2. What's up?
zuìjìn zěnme yàng? 最近怎么样? 'How are things lately?'
zěnme la? 怎么啦? 'What's up?'


3. Busy?
zuìjìn (gōngzuò) máng ma? 最近（工作）忙吗? 'Busy (at work) lately?'
zuìjìn máng shénme? 最近忙什么? 'What are you busy with lately?'

4. Other more specified questions
qù nálǐ? 去哪里? 'Where you going?'
huíjiā a? 回家啊? 'Going home?'

These expressions are for people you already know. Please don't ask a new acquaintance if he has eaten :)

More on greetings:
http://www.chineselearner.com/speaking/chinese-greetings.htm

You are learning Putonghua 普通话, not Hanyu 汉语

Chinese teachers, esp. those from China, use the term 'Hanyu 汉语' to refer to Chinese. I am not in favour of this because in reality no native Chinese (except teachers) uses this in a daily conversation. This term is rather historic. Hanyu, belonging to the Hanren (Han-people), was used to contrast with languages spoken by other ethnics, like Zangyu (Tibetan) or Mengguyu (Mongolian), that exist in China. Hanyu, just like Zhongwen 中文 (Chinese language, usually refers to the written language), can by and large include the regional dialects like Yue (Cantonese), Wu, Min, Hakka, etc. Hence, it is not appropriate for those who are learning only Mandarin Chinese.

I use 'Putonghua 普通话' (lit. common language), which refers to the official common spoken language in China. Taiwanese use 'Guoyu 国语' (lit. country language). Singaporean, Malaysian or overseas Chinese use 'Huayu 华语' (Hua - ancient term for China/Chinese). These are all acceptable depending where your teachers come from. Zhongwen is also commonly used.