Prepositions—little words that locate people, places, and things in time or space—can be really tricky, especially when we try to distinguish between the slightly different shades of meaning that different prepositions suggest to readers. Understanding how prepositions show relationships between nouns can help writers craft more effective sentences.
Common prepositions include on, in, to, at, and by, but prepositions also appear in phrases like between two ferns, via the Karakoram Highway, and Ali v. Frazier (where v. is an abbreviation for versus).
Common prepositions and the relationships they express: this Purdue OWL page offers examples of how common prepositions establish show relationships between people/things and other people/things.
A long list of common and less common prepositions: if you're looking for preposition options, start here. This thefreedictionary.com page offers clear, reasonably uncluttered, alphabetized lists of prepositions.
Usage and examples of all prepositions: the Merriam-Webster Learner's Dictionary offers help to all writers working to figure out the English language. Just type in a preposition from the lists above to see examples of how it is used.
Discerning between fine shades of meaning in preposition usage: try Google Books' Ngram Viewer feature, which allows you to test two or more versions of a phrase against each other to see which ones have been most used in more than eight million pre-2019 books. Ngram is not a perfect, complete, or up-to-date resource, but it's useful.
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Grammatically speaking: we still like this older resource on prepositions from Columbia College (in Sonora, California). It covers the basics as it helps writers identify prepositional phrases in sentences and offers advice on how prepositions can help in figuring out a sentence's subject(s).
Between v. Among: to do a really simple word fight (e.g., between v. among, or toward v. towards), try adding Grammar Girl to your search. Mignon Fogarty is a reliable resource. Here's what she says about prepositions (spoiler: the "secret weapon" she identifies on page 3 is Ngram).
Can I end a sentence with a preposition?: here's Grammar Girl Mignon Fogarty again.