Yin and yang are no strangers to English speakers. The dark and the bright. The cold and the warm. The chaos and the order.
Let’s get one thing out of the way: yang sounds like “young”. An a in pinyin always sounds like aah. Pinyin wasn’t designed with English in mind.
The concepts of 阴 and 阳 come from Taoism, a philosophy that has tremendous influence on the Chinese languages and cultures, but that few today actually understand. A typical Chinese person might not know much more about yin and yang than a typical Westerner, but they will know these words that involve this dual concept:
太阳
太阳 is the sun. 阳 is usually reduced to a natural tone, but when enunciating or in a theatrical setting, it might still be read in the second tone.
You might know 太 from phrases like 太好了！(Wonderful!) or 太大 / 太小 (too big / small). Its root meaning is “big” or “high” or “extreme”, frequently used as a prefix, such as 太空 (space, lit. “the big empty”), 太子 (crown prince, lit. “the high son”), or 太爷 (great-grandpa).
So 太阳 literally means “the big yang”. Guess what the moon is called? Did you say 太阴? Well, it’s not incorrect; people used to call the moon 太阴, but it’s become archaic. Today, most people know the moon as 月亮. As with 太阳, the second character is usually reduced to a natural tone.
By the way, 阴 and 阳 are the simplified forms of the two characters. 阴 used to be 陰, and 阳 used to be 陽. The simplified forms just took the characters for “the moon” (月) and “the sun” (日) and added them to the 阝radical.
山水
Literally “mountains and waters”, the word 山水 often just means “scenery” or “landscape”. Many Chinese cities are named after a river or a mountain, and they often specify which side of the mountain or river they’re on.
So which side is 阴 and which side is 阳? It’s actually quite straightforward: if you can see the sun, it’s 阳; if you’re in the shade, it’s 阴. Since China is in the northern hemisphere, the sun is often in the south. This means the south side of a mountain and the north side of a river are 阳; the opposites are 阴.
Some of the most famous cities named in this manner include 沈阳 (Shenyang, north of 沈 river) and 洛阳 (Luoyang, north of 洛 river).
阴性
In English, a medical test can come back negative or positive. In Chinese, it comes back yin or yang. 性 means “character” or “nature”. Literally, if your test came back negative, in Chinese you’d say it came back “with a yin nature”.
In this sense, 阴性 / 阳性 often goes with the verb 呈. This is quite a literary word that usually means “to humbly submit” (a letter or an application); it’s also often used to mean “to look” a certain way, as in “the city looks festive during the holidays”. To say a test came back negative, you’d say 检测呈阴性.
In linguistics, 阴性 / 阳性 also refers to a word’s gender, feminine or masculine, in languages that have them. For example, in German, die Stadt is 阴性, der Hund is 阳性, and das Buch is 中性.
阴谋
Who doesn’t love a true crime documentary? In Chinese, 阴谋 is how you say “a conspiracy”. 谋 means “to plan” (as a verb) or “a plan” (as a noun), as in the chengyu 不谋而合 (“no plan but join”, to happen to have the same thought or behavior without having had a discussion first). A conspiracy is “a plan in the shade”.
People do sometimes use the word 阳谋, but you might not find it in the dictionary. 阴谋 tends to be secret, and tries to retain the element of surprise; the English word conspiracy carries this connotation of secrecy too, but one doesn’t have to be secretive to be legally charged with conspiracy. 阳谋 on the other hand is a plan out in the open. It’s a trap that the enemy knows about but still can’t help but step in.
Bonus: 阴阳怪气
Supposedly, 阴阳怪气 was a word coined in the 1940s by the playwright 曹禺 in his three-act play 《北京人》(Beijing People). Literally “yin-yang-strange-air”, it originally describes a person whose attitudes towards things are ambiguous, whose words and behaviors are secretive, and just overall eccentric.
Modern usage of this word tends to describe a person whose tone of voice is overly sarcastic or acrid, out of spite or out of jealousy. For example, if you’re showing off your new car to your neighbor, and instead of congratulating you, they said, “goodness me, you spent half a year’s salary on this broken toy? You gotta have that noggin of yours checked out.” Then you could rightly describe your neighbor as being 阴阳怪气.
This is a bit different from its original usage, and I think the word took on this new meaning through a reinterpretation. 怪气 (strange air) seems to suggest a remark that came out of nowhere (“why would you say such a thing”), and 阴阳 seems to describe the actual fluctuations in a sarcastic tone of voice: it goes up and down and up and down, like YoU gOtTa HaVe ThAt NoGgIn ChEcKeD oUt.
At least that’s my understanding. If you feel differently about how this word came to mean what it means today, feel free to comment below.
D. R. Whispers 
阴阳怪气的“怪气”于我更像是“语气作怪”的意思。