For rules concerning the use of hyphens, see CMS 6.75–6.77 and especially CMS 7.77–7.85. See also the CMS hyphenation table, publicly available via PDF. Some general rules of thumb follow.

In nouns

Check the American Heritage Dictionary, which can be useful for noun forms that are evolving into being hyphenated or being written as one word in common practice.

In adjectives

In general, omit hyphens from compound adjectives unless the absence of the hyphen will cause confusion. For example, most readers are not likely to be confused by the lack of hyphenation in “money management strategy.” Do hyphenate something like “moving-average method,” which might otherwise be interpreted as “an average method that causes great emotion.”

We hyphenate comparative and superlative forms of compound adjectives when the simple form is hyphenated and/or when the absence of the hyphen could be confusing.

Examples: “well-qualified manager,” so “better-qualified manager” and “best-qualified manager”

Avoid, wherever possible, more than one hyphenated adjective in a row. Perhaps some of that description can be switched to the other side of the noun, where it won’t need to be hyphenated, even if the sentence becomes wordier.

Example: a “long-billed, cotton-pickin’, New Zealand–born kiwi bird” rephrased to have only one hyphen is a “long-billed kiwi bird from New Zealand that picks cotton”