Since there are On and Kun readings for kanji, does it mean that every word that can be written with kanji has two ways of pronouncing it?
No, most Japanese kanji words have only one correct reading. For example, the correct reading of 電車 is always でんしゃ. Just because a character can be read in two ways does not mean a word using that character can be read in two ways. In partucular, many on-readings make sense only as part of longer compounds.
However, some kanji words do have multiple possible readings, and you have to determine the correct reading from the context. For example, please see: Difference between こんにち and きょう
Note that the number of such words is not large, and that English also has a similar problem (e.g., "lead", "wind", "minute", and many more).