I made a video talking about many aspects of one kanji, 人. I chose it because it is a frequent subject of questions here.
I included facts that even advanced learners might not know, but if you just want the TLDW on the rules of thumb for readings, they are as follows.
Rule 1: にん is used for counting, and じん is used for place names.
Rule 2: When 人 follows a 2 character compound that uses onyomi OR a word that uses kunyomi, the reading of にん is used when the word expresses an action (e.g. 案内人).
Rule 3: When 人 follows a 2 character compound that uses onyomi or other word, the reading of じん is used when the word expresses an attribute. Those attributes can be related to location, occupation, or other traits (e.g. 有名人).
Rule 4: When 人 makes a 2 character compound with another kanji (e.g. 他人), the reading cannot be reliably predicted. These words’ readings are usually based arbitrarily on when the word was imported from Chinese, or other individual circumstances for particular words. Unfortunately, a great number of words fall in this category, and I think it is an overzealous application of rules 2 and 3 to these words that gives the sense that the rules are unreliable or full of exceptions.
The sources I used for the video are listed in the description on Youtube.