The Chicago Manual of Style contains a huge chart listing various sorts of phrases which are or are not to be hyphenated. Consult such a reference source for a thorough-going account of this matter, but you may be able to get by with a few basic rules. An adverb/adjective combination in which the adverb ends in -LY is never hyphenated: "His necktie reflected his generally grotesque taste." Other sorts of adverbs are followed by a hyphen when combined with an adjective: "His long-suffering wife finally snapped and fed it through the office shredder."
Adjectives combined with nouns having an -ED suffix are hyphenated: "Frank was a hot-headed cop."
Hyphenate ages when they are adjective phrases involving a unit of measurement: "Her ten-year-old car is beginning to give her trouble." A girl can be a "ten-year-old" ("child" is implied). But there are no hyphens when outside of such an adjectival phrase: "Her car is ten years old." Fractions are almost always hyphenated: "He is one-quarter Irish and three-quarters Nigerian." The exception is when the numerator is already hyphenated, as in "ninety-nine and forty-four one hundredths."
A phrase composed of a noun and a present participle ("-ing" word) must be hyphenated: "The antenna had been climbed by thrill-seeking teenagers who didn't realize the top of it was electrified."
These are the main cases in which people are prone to misuse hyphens. If you can master them, you will have eliminated the vast majority of such mistakes in your writing. Some styles call for space around dashes (a practice of which I strongly disapprove), but it is never proper to put space around hyphens.
List of errors