Reading kanji

I’ve been watching Japanese shows for almost a decade now and I’ve always wanted to know - how do the Japanese read Kanji?

For example, the kanji 力 (can mean either, force, power, or strength) can be read as "riki" or "chikara." I understand that certain readings are used in certain contexts but how can anyone be sure? For example, in the Police batsu, Endo’s booklet contained an apparently difficult-to-read kanji (the 率 in 率先, read as "sossen") but he remembered to double the "s" in "sen." I have no idea how to word this…

Also, when it comes to compounds, how are those read? The rules seem all over the place.

Most kanji have two kind of reading types: kun-yomi and on-yomi. On-yomi are usually used in compound words and kun-yomi with single words.
For example, 先 is often read as "sen" in compound words (like sensei or senpai, respectively 先生、先輩) but by itself it’s read as "saki" ("first", "ahead", "previous" and many other meanings).
The "doubled s" in your example comes from the reading of the previous kanji 率, which has many readings (like "ri+つ", "so+つ" and "shu+つ") that make the next syllable’s consonant to be geminated.

And yes, the rules are all over the place. The only way to know certain compound readings is memorizing them. Even the Japanese themselves spend a great amount of time in school to learn all basic kanji (the 2,136 characters known as the "jouyou kanji").

Sorry for bumping, but I made this because I like reading into Japanese games, like rivals and their names and stuff. Anime and racing games come up in particular, because a lot of names that are made of unique kanji compounds come up.

A good example is the first "real" boss in Tokyo Xtreme Racer Zero, whose name in Japanese is 迅帝. The translators interpreted the name literally as "Speed King" but in the sequel I found out his name was read (and romanized) as Jintei. When I look up the first kanji, it’s normally read as "jin" but can also be read as "shun" or "Shin." What do I do then, with made-up compounds like those? Do I just go with the most common readings for both kanji? There was no furigana or anything so I was stumped when I found a video of the Japanese version.