To hyphenate or not?

Asking for something that is both concise and comprehensive is, unfortunately, contradictory. The Chicago Manual of Style, 14th Edition devotes one full page (5 numbered sections, 6.38-42) to "general principles" of hyphenating compound words, but then also goes on to list a 13-page table of common forms, when to hyphenate them, when not to, and when to make exceptions to other parts of the table.

To summarize the relevant segments for you, though (my additions in [brackets, italicized]):

6.38: The trend in spelling compound words has been away from the use of hyphens; there seems to be a tendency to spell compounds solid [i.e. unhyphenated] as soon as acceptance warrants their being considered permanent compounds.

6.39: When a temporary compound is used as an adjective before a noun, it is often hyphenated to avoid misleading the reader. (e.g. "a fast sailing ship": is it a "ship that is sailing fast", in which case you should hyphenate it, or "a sailing ship that is fast", in which case you should leave it unhyphenated.)

6.40: Where the compound adjective follows the noun it modifies, there is usually little to no risk of ambiguity or hesitation, and the hyphen may be safely omitted. [There are, of course, exceptions to this, as in "her reply was thought provoking."]

6.41: [contrary to its earlier positions,] The University of Chicago Press now takes the position that the hyphen may be omitted in all cases where there is little or no risk of ambiguity or hesitation.

6.42: There are scores of other rules for spelling compound words, but many of them are all but useless because of the multitude of exceptions. See table 6.1 [that 13-page behemoth of a table mentioned above] for some of the more dependable rules.