How many ways are there to say "Chinese?"
Well, I haven't counted yet, so I don't know. But I think it's quite a few. Let's start with number
1) 中文 Zhong1中(Middle) Wen2文(Text, Language). The first Character here stands for the word for China: Zhong1中(Middle) Guo2国(Country).
2) 汉语 Han4汉(The Han nationality) Yu3语(Words, Language). This one is pretty easy to understand, the majority of Chinese people are Han, and the word Yu3语 stands for the full word Yu3语 Yan2言 which means language.
3) 普通话 Pu3普(Ordinary) Tong1通(Communication) Hua4话(Speech). The first two characters together 普通 mean common, or ordinary, and the character 话hua4 means speak, as in the word 电dian4话hua4 or 'electric speak' = telephone. The reason Chinese might be called putonghua 普通话 is that there are so many dialects...but when people say 'Chinese' they mean the common or standard variety. It's also worth noting that some Chinese characters like the word 通 above have so many meanings that it is basically useless to try to translate the single Character, instead it is used almost exclusively in combination with another (or several) Characters.
4) 国语 Guo2国(Country) Yu3语(Language). This one is easy, the 'offical language of the country' is obviously Chinese. One annoying thing that Chinese people often say is 'Wo3我(My) Guo2国(Country)' which just means 'China.' And it's said not just by individuals, but in essays or written into the evening news.
5) 中国话 中1Zhong 国2Guo 话4Hua. It's almost unnecessary to put the english, as all these characters were already explained above. The first two together 中国 mean China and 话 means speech. I like this one best, maybe because it's also the title of a Chinese pop song.
Ok, so the answer is '5' common ways of saying "Chinese."