German prepositions govern different cases. That is, the phrase that follows them will be in either the accusative case, the dative case, or the genitive case. Memorizing which case each preposition governs is not critical for reading comprehension, but you should be aware that articles, pronouns, and adjectives will change form after the preposition. If you wish to know which case(s) a preposition governs, refer to your dictionary.
Rarely, you may encounter situations where case does matter for reading comprehension. The meaning of a certain group of prepositions – the so-called "two-way prepositions" (an, auf, hinter, neben, in, über, unter, vor and zwischen) – changes subtly depending on whether the accusative or dative case is used after them. If you see accusative case, then a changing condition is being described. If dative case, then a static, unchanging condition. Normally the rest of the sentence will clarify the preposition’s meaning for you, but in a few circumstances, mainly relating to physical movement or location, you may be left unsure, and you will need to consider the case as useful information. For example:
Er geht in das Haus.
He walks into the house.
Note the accusative case. Here a change is being described, from "not in the house" (before) to "in the house" (afterwards). Compare to:
Er geht in dem Haus.
He is walking, in the house.
Note the dative case. Here there is no change regarding the state of being "in the house." In English we don’t have this clarity, so you may need to take extra care to communicate this in your translation. The second sentence could also be translated as: "He is in the house, walking," or, using parentheses to acknowledge that we’re embellishing the sentence: "He walks (around) in the house."