How do you use the accusative prepositions? What do they do?
I think that it is better to look at the big picture , not only at the accusative prepositons. All of the prepositions change the case of the noun which follows them. The noun will be either in the accusative, dative or genitive case instead of the basic nominative case.
Here is a pretty good overview: https://en.wikibooks.org/wiki/German/Grammar/Prepositions_and_Postpositions
Maybe it helps if you think about personal pronouns in English - they are also declined after all prepositions in a similar way as all nouns are declined in German. However, in English there is just one "case" which is close to the German accusative case:
- That man came before me (you cannot say before I).
- Give the phone to him (you cannot say to he).
- This chocolate is for her.
- This happened because of them.
All prepositions require the following noun/adjective to have some case. Some have multiple options: normally dative or accusative. If there is no choice, the meaning of the preposition is completely determined by the preposition itself, and the case does not "do" anything. If there is a choice, the case may determine the exact meaning of the preposition, e.g. dative for static position vs. accusative for motion.
In German an unlike in English, the verb determines the case of the following object. As in English, many verbs have fixed prepositions that need to be memorised with the verb. Here is a list: https://www.deutschakademie.de/online-deutschkurs/forum/index.php?topic=86.0