I’ve not written about this subject, but I’ve seen blogs and more needs saying.
Prepositions AT THE END OF THE SENTENCE. When one of his sentences was corrected on this point, Winston Churchill responded: “This type of arrogant pedantry up with which I will not put.”
There is a common usage in American to ADD A PREPOSITION to indicate direction, although the direction is inferred from the verb; the preposition is not necessary. The usage should be “stand,” rather than “stand up.” Likewise, usage should be “sit” rather than “sit down,” unless you’re giving instructions to an obstinate dog or a troublesome kid.
Prepositions can simplify paragraphs especially when giving the RELATIONSHIP of a thing, a person or a place to another. Consider: below, above, behind, ahead, under, with, beside. Prepositions can be used LIKE A VERB to connote motion or activity: up, through, from, along, over, to and toward.
In University studies of FOREIGN LANGUAGES (French, German), I learned that this preposition was used only with this verb. Other prepositions used with that verb were wrong. English is more relaxed. I’ve never seen a list or a reference book. The rule apparently is, just like the controlling rule for all writing in this language, use which ever preposition that makes sense and conveys the meaning you want.