approach has 21 distinct synonyms spread across 12 of its 14 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
ideas or actions intended to deal with a problem or situation
“his approach to every problem is to draw up a list of pros and cons”
the act of drawing spatially closer to something
“the hunter's approach scattered the geese”
the final path followed by an aircraft as it is landing
a tentative suggestion designed to elicit the reactions of others
“she rejected his advances”
the temporal property of becoming nearer in time
“the approach of winter”
a close approximation
“the nearest approach to genius”
a relatively short golf shot intended to put the ball onto the putting green
“he lost the hole when his approach rolled over the green”
come near or verge on, resemble, come nearer in quality, or character
“This borders on discrimination!”
Synonyms, antonyms and the broader and narrower relations for approach come from Princeton University’s WordNet. Full sources and licences.