If two words are used together to form an adjective, they are often hyphenated (unless the first one ends in “-ly”). If the same two words are used in adverb form, they most often aren’t hyphenated—instead they are used as two individual words. It’s probably safest to consult The Chicago Manual of Style (7.90 in the fifteenth edition) for each individual case if questions arise.
A common question regarding hyphenated compound words involves capitalization in titles. Although the fifteenth edition of Chicago goes with capping the first word and lower-casing the second, the Office of University Marketing caps both words. We’ll follow the university marketing guide and cap both words (e.g., Natural-Born Cyborgs. This is a change from the past but follows the university style guide and just tends to look better in most cases.
Some examples of nonhyphenated compound words we may encounter include
testbed (to agree with NSF)