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The accusative in German is used to describe the direct object in a sentance:

I gave the horse an apple
^ Nom   ^Dat     ^Acc

Nom: Nominative
Dat: Dative
Acc: Accusative

After the prepositions:

vor
hinter
über
unter
zwischen
neben
in
an
auf

It is used when motion towards is implied. The dative is used when no motion is implied.

Gehen Sie hinter den Bahnhof.

Go behind the railway station.

In addition, it is always used after these prepositions:

durch
ohne
gegen
wider
um
für
entlang
bis
I have recently been told how to remember these by a German teacher. By the acronym DOGWUFE (Think "Dog Woofer"). Of course he doesn't seem to have included bis in there... Perhaps this is because it is very often used before another prepositon. At least I hope that's why. Certain prepositions can be contracted, some common ones are listed below:
an das  -> ans  
in das  -> ins 
auf das -> aufs

Gender  Nom Acc
Masc    Der Den
Fem     Die Die
Neut    Das Das
Plur    Die Die

The accusative is simple to remember, as there is only one change, the masculine definite article, changes from der to den.

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