1. A compound adjective is formed when two or more adjectives work together to modify the same noun. These terms should be hyphenated to avoid confusion or ambiguity.
Incorrect: The black and blue mark suggested that he had been involved in an altercation.
Correct: The black-and-blue mark suggested that he had been involved in an altercation.
Incorrect: Her fifteen minute presentation proved decisive to the outcome of the case.
Correct: Her fifteen-minute presentation proved decisive to the outcome of the case.
2. However, combining an adverb (usually a word ending in "ly") and an adjective does not create a compound adjective. No hyphen is required because it is already clear that the adverb modifies the adjective rather than the subsequent noun.
Incorrect: The remarkably-hot day turned into a remarkably-long week.
Correct: The remarkably hot day turned into a remarkably long week.
3. Furthermore, you should not place a hyphen in a compound adjective if the adjectives are capitalized, such as when they are part of a title.
Correct: His book was entitled, "Gender Neutral Language in English Usage," and it revolutionized the way people think about sex roles.
However: His book on gender-neutral language revolutionized the way people think about sex roles.
Correct: The students were participants in Chicago-Kent's vaunted Legal Research and Writing Program.
The student decided to attend a school with a good legal-research-and-writing program. Note that in this example, the reference is to a type of program, rather than a specific program, and so the use of hyphens is proper.