When seeing a new Kanji, are there clues in the Kanji that give you an idea as to what it means? If so, what are the clues and where can I learn them?

For instance, in English I can see the word “monolingual” and know it has something to do with one (mono) and language (lingual). Does something like this exist for Kanji? How can I learn these “fundamentals” of Kanji?

by SoopaTom