Prepositions have more than one function. They often accompany a verb. Unfortunately they often lose their meaning if they do so. The Germans say:
Ich warte auf den Bus. I am waiting ,on' the bus.
which doesn't mean that someone is sitting on the bus roof. These prepositions are also followed by a dative or accusative case. The good news is, that you already know by which one, thanks to the preposition lessons from earlier.
Just the two-way prepositions cause trouble, because now the questions Wo? and Wohin? don't make any sense. In the sentence
Ich denke an meine Mutter. I think ,at' my mother.
it doesn't make any sense to ask Where do I think? or Where to do I hink?
After vor, hinter, über, unter, neben, an, zwischen, auf and in NOW you simply use the Accusative and you’ll be correct in 95% of the cases. Meaning that you are left with only about 20 verbs + two-way prepositions + dative. Learn these and you are done with this part of the problem. Of course you`ll find a list of them in the back of this book.
Let’s take a look at a few examples. Note that the English samples are often not direct translations but rather memory-aids in English that are thought to simplify your work.
warten auf wait for > Er wartet auf den Aufzug. He waits for the offer
denken an think of > Anna denkt an ihre Karriere. Anna thinks of her career.
bitten um ask for > Er bittet um einen Umhang. He asks for a lumberjack.
Why are these examples better than others?
First of all, they make as much sense as any other example, so there is no disadvantage. These examples have built-in clues about what the preposition of the verb might be. As you can see, parts of the words are highlighted. These parts resemble the preposition that has to be learned with this verb. The words Aufzug, Anwalt, Umhang respectively: offer, Anna, lumberjack are easier to memorize and more likely to be remembered than the abstract prepositions auf, an, um.
Download a list of the most common verbs with prepositions here:
I'm not a big fan of lists but many learners like them. My problem with lists is that if you just memorize their content, you'd just be learning random words completely out of context. But if you use this list mainly for your preaching, you should be okay.
This topic is covered in: A2-L34