Prepositions require either the dative case, the accusative case or (less common) the genitive case. "Für", for instance, requires the accusative case. A good dictionary will tell you which case is needed when you look up the preposition.

Most prepositions like "für" can be followed by only one case. However, a certain group of prepositions called "two-way prepositions" can be followed by either the dative case or the accusative case depending on whether they indicate a fixed location (dative) or motion (accusative).

Ex. 1 "Ich bin in EINEM Haus" (I am in a house. Fixed location - dative).

Ex. 2 "Ich gehe in EIN Haus" (I go into a house. Movement - accusative).

Dative prepositions: aus, außer, bei, mit, nach, seit, von, zu, gegenüber

Accusative prepositions: durch, um, gegen, für, bis, ohne, entlang [when used as an accusative preposition, "entlang" comes after the noun, e.g. "die Straße entlang" = along the road]

Genitive prepositions: anstatt, statt, außerhalb, innerhalb, trotz, während, wegen

Two-way prepositions: vor, hinter, über, unter, neben, an, zwischen, auf, in

See also:

http://duolingo.com/#/comment/33770

http://german.about.com/library/blcase_dat2.htm

http://german.about.com/library/blcase_acc2.htm

http://german.about.com/library/blcase_gen2.htm

@Katherle.....thanks for the very informative post. (there seems to be a great deal to memorize).