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.