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)
• antibiotic

but

• anti-inflation
• anti-junta
• anti-ageism
• anti-racism
• anti-Semitic

Use a hyphen with the prefix "re" where the word would otherwise be confusing.

• re-admission
• re-entry
• re-coiled the rope (as opposed to recoiled in horror)
• re-covered a chair (as opposed to recovered from an illness)