Ah, yes, prepositions. Tiny little words with great big importance. If we didn't have prepositions, we wouldn't be able to go in the house, or over the fence, or with the dog, or without the dog, or . . . well, you get the idea. Using prepositions in English is very easy as compared to their usage in German, where knowledge of the accusative, dative, and genitive cases is needed in order to understand how to use them. Thus, it is customary to divide German prepositions into groups based upon which case they are associated with. The subsequent sections follow this traditional method.
It is also important to note that there isn't always a literal one-for-one equivalent between an English preposition and a German preposition. This is another source of frustration for students of German, as many German prepositions have to be learned in a specific context. For example, the English preposition to has many equivalents in German, such as zu, nach, an, auf, and in, the proper use of which depends on context and sometimes even on which type of noun is in the phrase. Frequent practice is really the only way to get them all down.