Use hyphens to join together separate words to make them into a single adjective.
Zaphod shook his head with a tight-lipped smile.
The right-hand head seemed to be thoroughly preoccupied with this task, but the left-hand one was grinning a broad, relaxed, nonchalant grin.
When an age is used as an adjective, put hyphens between the words.
The three eleven-year-old students walked up the steps to the Great Hall.
When a prefix ends with the same letter that the root word starts with, use a hyphen to join them.
anti-immigrant, pro-orthodox
When self or ex are used as prefixes, they are often attached with hyphens.
self-absorbed, self-respect ex-marine, ex-wife Zaphod Beeblebrox, adventurer, ex-hippy, good timer, (crook? quite possibly), manic self-publicist, terribly bad at personal relationships, often thought to be completely out to lunch.
Use a hyphen to join the words for the tens and ones place in numbers, and to join the numbers in a fraction.
two thousand, six hundred, eighty-five three-fourths, seven-ninths
When you have two prefixes for one word, use hyphens after each prefix.
The pro- and anti-American forces clashed.
☠Do NOT use hyphens to split words into pieces when you run out of room on a line. Instead, write the whole word on the next line.