Prose is a format of language that features ordinary grammar and sentence structure as a rule, though many stream-of-concious and experimental/postmodern novels subvert these norms. It is most commonly seen in day-to-day communication (emails, notes, many novels, etc.). Prose is flexible - it can be as informal as a scribbled note or first-person young adult novel, or as formal as a political speech or dissertation. Generally speaking, however, it does not require the measured metre and rhyme schemes found in much poetry. Some examples of different forms of prose include nonfiction such as essays, speeches, journals, biographies and articles, and fictional forms, such as genre, heroic, literary and dramatic prose as well as fairytales and fables.
Fiction is any form of work that features or is based on information that is not real or incorrect. Usually, fiction is creative and hypothetical, and it can be both literary or cinematic/genre. Three degrees of fiction are: realistic, semi-realistic and non-realistic. Realistic fiction is plausible, but still not factual, semi-realistic pushes the boundaries of believability a little further and non-realistic can be utterly fantastical and downright surreal. Often, fictional works find a basis in real life, such as some scientific phenomena or historical event, but expound on it to create magical or futuristic events and consequences to allow for author creativity and better storytelling. Popular fictional prose today includes Tolkien's well-loved The Lord of the Rings trilogy and J.K. Rowling's more recent record-breakers, the Harry Potter series.
Non-fiction prose is any work that consists of only factual or real-world information. There is usually historical or empirical data available to prove the validity of non-fiction works, though speculative articles and essays may also fall under this banner so long as their uncertain aspects are not hidden. These works tend to be narrative as well - a dictionary or constitutional document would not usually be categorized as nonfiction prose, but rather a reference or political document. Works of nonfiction can be found everywhere, from the biographies of famous people to any given article in your news source of choice, one would hope.