非 + [noun] / [adjective]
[subject] + 非 + [noun]
非 means "not" in written Chinese. Its most frequent job is as a prefix, like English "non-" or "un-": 非 + a noun or adjective names everything outside that category.
The usual shape is 非 + a two-syllable word: 非正式, 非官方, 非营利, 非专业, 非紧急. A few have become words of their own, such as 非法 "illegal". 非常 "very" also began as 非 + 常, but is now a plain adverb of degree.
In formal writing and set phrases 非 can stand for 不是 before a noun: 成功非一日之功 "success isn't one day's work", 答非所问 "an answer that misses the question". In most sentences this is done with 并非 or 绝非, which have their own entry.
Before a verb, 非 is short for 非…不可 "must, insist on", which has its own entry. To say an action doesn't happen, use 不 or 没.