The name Chinese Medicine in Chinese...

針術 is a way to write acupuncture in Chinese.

The first character means “needle” or “pin.”
The second character means “technique” or “method.”

This is theoretically a Japanese word as well but not commonly used.

針療法 is one of two ways to write acupuncture in Chinese and Japanese.

The first character means “needle” or “pin.” The second character means “to treat” or “to cure.” The last character means “method” or “way.”

This is the only reasonable selection if your audience is Japanese. This is the formal way to express acupuncture in Chinese, so this version is universal in most of Asia (the best all-around choice in most cases).

鍼灸 is the Chinese, Japanese Kanji, and old Korean Hanja word for acupuncture-moxibustion.

醫道 means the art of healing or medical skill.

This can also refer to a Korean TV show, Hur Jun about an ancient doctor. The Chinese-subtitled version of the show is also quite popular in China.

While this is a common title in Chinese and Korean, it's not used as often in Japanese where someone might read it as “medical course” or “the way of medicine.”

中醫 is how to write “Chinese traditional medicine.”

The original medicine consists of herbal remedies derived from over 3000 years of research.

醫生 is the title used to refer to medical doctors or physicians in China.

Note: Sometimes, this same term is used in Korean, but not common.

The meaning is close to “healer [of] life” as the first character, 醫, can mean medicine, the healing art, healing, curing, medical, to cure, or to treat. The second character, 生, means birth or life.

In Japan, they use a simplified version of the first character (医生 is also used as the Simplified Chinese version of Doctor). If you want this version, please click the characters to the right instead of the button above.

妙手仁心悬壶济世 is a phrase that celebrates the benevolence, skill, and service to his/her patients.

Here's a breakdown of the characters:
妙手 miào shǒu admirable skill in curing disease (when used in reference to doctors).
仁心 rén xīn kindheartedness, charity, benevolent heart.
悬壶济世 xuán hú jì shì practice medicine or pharmacy to help the people or the public.

精, 氣, 神 are the characters jing, qi, and shen.

As a set, these three characters are known in English as the treasures of traditional Chinese medicine, the treasures of Qi Gong, or the three treasures of Taoism / Daoism.

Sometimes this set is titled 三寶 (sānbǎo) or “three treasures,” but here, we're writing each treasure out.

Here's how these characters are perceived in this context...
Jing: nutritive essence; refined; perfected; pure
Qi: vitality; energy; force; breath; vigor
Shen: spirit; soul; mind; being

To keep it simple, you can use “essence, vitality, and spirit” to define these.

茶 means tea. It can refer to prepared tea (ready-to-drink) or dry tea leaves.

The origin of tea is China but the same character is used in Japanese Kanji, and old Korean Hanja with the exact same meaning. Japanese and Korean even borrowed the pronunciation from Chinese (pronounced “cha” in all three languages).

It's said that an early doctor (or herbologist) in ancient China kept poisoning himself as he tried different new herb concoctions. He invented tea as a means to detoxify himself as he recovered from 1 of the 76 times he nearly poisoned himself to death. Tea is seen not just as a drink but as a form of medicine used to remove impurities from the body.

The word “chai” (used in many languages to refer to various teas) is derived from this Chinese word.

茶 also means camellia, as Asian teas are often based on the leaves of camellia plant varieties.

三寶 is the title for “Three Precious Treasures of Buddhism” or “The Triple Gem.”

These three treasures are the Buddha 佛, the Dharma 法 (teachings or the law of the Buddha), and the Sangha 僧 (the community of monks or followers).

This term is used by most (perhaps not all) Buddhists in China, Japan, and South Korea (written the same in the original form but pronounced differently in each language). Non-Buddhists may just read this as “Three Treasures” without the religious context. For instance, there is also a “Three Treasures of Chinese Medicine” that is sometimes titled the same way.

In modern Japanese and Simplified Chinese, this is written 三宝 instead of 三寶.

華佗 or Hua Tuo was a Chinese physician who lived during the late Eastern Han dynasty.

The historical texts Records of the Three Kingdoms and Book of the Later Han record Hua Tuo as the first person in China to use anesthesia during surgery.

Hua Tuo used a general anesthetic combining wine with a herbal concoction called 麻沸散, literally, “cannabis boil powder.” This was in the second century AD, almost 1700 years before western medicine had any form of anesthesia (1846).

致道館 is the name Chidokan.

Chidōkan was established in 1805. The original Chidōkan school was located in Tsuruoka, Japan.

The original school taught a combination of traditional Chinese literature, Ogasawara-ryū etiquette, Chinese medicine and martial arts alongside Confucianism.