I was confused about Kanji and readings for weeks a few years ago. This is my advice:
Don’t try to memorise readings (pronunciation). Kanji represent concepts. 山 represents the concept of a mountain, for example; 書 represents the concept of writing. Now that we know that, we can take a look at the words that the Kanji is used in. You have to remember that Japanese was a written language for a few thousand years before they stole the Chinese characters over a millennia, incorporating them into the language and creating some of their own characters. Kanji were created to accommodate the words that already existed in the language; not sounds.
Now that we know that 山 represents a mountain (i.e. the meaning of the kanji), we take a look at the words that Kanji is used in. One word it is used in is やま, which is written 山. Another word is とざん, which is written 登山.
Yet, the on-yomi readings are ‘さん’ and ‘ぜん’, so why is it read as ‘ざん’ in this word? Truth is, readings are only really helpful in guessing how it might be read in a word.
It’s pretty pointless to learn the readings of a Kanji; instead, you should learn the meaning of a Kanji, and then learn a number of words that are written with that Kanji and how that Kanji is pronounced in each word.