The characters three languages share

Japan borrowed Chinese characters twice over, and kept both halves: the Chinese pronunciation, worn down by 1,500 years of Japanese mouths (音読み on'yomi), and the native Japanese word for the same idea (訓読み kun'yomi). That is why every kanji has at least two readings — and why one of them is a cousin of the Mandarin and Cantonese words. 山 is san in Japanese, shān in Mandarin, saan1 in Cantonese. Learn the character once; you get a foothold in three languages.

Play the readings back to back and a pattern appears: Japanese on'yomi often matches Cantonese more closely than Mandarin, because Cantonese kept the final consonants that Mandarin lost. 一 ichi / jat1 both end in a stop; Mandarin yī does not. Japanese borrowed these words when Chinese still sounded closer to Cantonese than to today's Mandarin.

On'yomi or kun'yomi — which one do you say?

The rule of thumb that gets you most of the way: a character on its own usually takes the native kun'yomi (山 = yama), and a character in a compound with other kanji takes the Chinese on'yomi (富士山 = Fuji-san, 火山 = kazan volcano). It is the same instinct as English using native words in speech and Latin ones in compounds — fire mountain vs volcano.

Same character, three simplifications

Japan and mainland China each simplified the traditional forms, separately and inconsistently, while Hong Kong and Taiwan kept the originals. So one character can have three shapes: 讀 (traditional) → 読 (Japan) → 读 (mainland). Others agree: 國 became 国 in both Japan and China. The table above flags every case where the shapes differ, which is exactly where a reader of one language stumbles over another.

Related: the 214 keys these characters are built from · hiragana and katakana, the two syllabaries Japanese uses alongside kanji · words the world shares.