Use a hyphen when you join two words to form an adjective. This eliminates confusion.
- first-year course
- full-time equivalent
- third-year students
- part-time studies
- the government-mandated budget cut
Use no hyphen when the meaning is clear and there is no ambiguity.
- one half course
- a full course
- one half of the students
Never use a hyphen where an "ly" adverb modifies an adjective:
- fully grown cat
- barely readable document
A hyphen should not be used to join a prefix to a root/base except to avoid doubling a vowel, tripling a consonant, duplicating a prefix or when the context is confusing or causes ambiguity.
- anticlimax (a familiar term, requiring no hyphen)
Use a hyphen with the prefix "re" where the word would otherwise be confusing.
- re-coiled the rope (as opposed to recoiled in horror)
- re-covered a chair (as opposed to recovered from an illness)