I will list here some of the most common prepositions used everyday along with the cases that the noun following them requires.
PREPOSITIONS WITH GENITIVE:
bez - without
blizu - close to
do - until, to, next to
duž - along
ispod - under
iz - from, out of
iza - behind
između - in between
iznad - above
nakon - after
od - from
oko - about
osim - except
poput - like
pored - next to
PREPOSITIONS WITH DATIVE:
k(a) - to [use 'ka' if the following word begins with: s, š, z, ž, ps, ks; otherwise use 'k']
nasuprot - opposite
unatoč - despite
usprkos - despite
PREPOSITIONS WITH ACCUSATIVE:
kroz - through
na - onto
u - into
za - for
PREPOSITIONS WITH LOCATIVE:
na - on
o - about
prema - towards
u - in
PREPOSITIONS WITH INSTRUMENTAL:
nad - above
pod - beneath
pred - in front of
s(a) - with [use 'sa' if the following word begins with: s, š, z, ž, ps, ks; otherwise use 's']
Not all prepositions are listed here. These are just the basic ones to get you started. Soon, I will explain how to decline nominal words (i.e. how to change their cases)as it's one of the most important aspects of Croatian.