This is a complicated and long topic that this author won’t go into huge detail here. This page has much better information, and you should read it carefully. But in the interest of not saying “Hey, go there” and having some interesting info here, you can read on for a summary.
Kanji is generally presented as a bunch of ideographs that you have to learn individually. Soon, you’ll start to distinguish patterns – they’re built off a series of “radicals”, each one having their own Japanese name. But even then, how they’re built and how to pronounce them can seem inscrutable at times. This is because you’re generally just taught them as a discrete component, and the patterns behind them are non-obvious.
Some kanji or jyukugo truly aren’t obvious. In the word “sushi”, for example, the kanji were chosen solely for their pronunciation, and have little to do with the actual meaning of the word. So there’s not any silver bullet. But you’ll find that most kanji have clues as to their meaning and their pronunciation built into them, if you know where to look and how to interpret them. This is why pages such as the one linked above are so valuable – they can take most, but not all, (well, some, at worst) of the guesswork out of learning the kanji, and make them a little more approachable.