Prepositions are words like in, on, outside, with and so on. Croatian prepositions have the added complexity that words following a preposition require a specific cases depending on the preposition and sometimes the meaning required.
There are a lot of prepositions, but most are followed by the genitive, so if you don't know the appropriate case to use, the genitive is a sensible guess. That said, you need to learn (at least) the preopositions on the first part of this page, which are all very commonly used.
blizu centra near the centre
Do followed by the genitive has the meaning 'up to, as far as'.
do kraja 'until (to) the end'
do oceana 'until (to) the ocean'
Do is also used when telling the time.
Radim do pet poslijepodne 'I work until five in the afternoon'.
Ja sam iz Engleske I am from England
Kod has a different meaning depending on whether it is followed by the dative or genitive.
Idem k roditeljima I'm going to my parents
kod kuće sam I am at home
kod zubara at the dentist
o čemo about what
o našim projektima about our projects (M. pl)
Od also has the meaning 'by' as in the song writen 'by' a specific musician.
Na and u which need to be looked at together. Unfortunately.
The verb ići (to go) with the prepositions u (in/to) and na (on/to) and the accusative case indicate movement to a particular destination.
So when do we use u and when do we use na?
The general rule appears to be that if the destination is a closed space (a house, a room, a building and so on), the preposition u is used, and in general u seems to appear more frequently.
It is a general rule only, as in Croatian parks and cities seem somehow to be considered as enclosed spaces according to this rule. Idem u park (I go to the park) and Idem u grad (I go to the city).
kroz prozor (through the window)
And na is used if you are climbing something or heading to an open space (but see above).
Na is is also used if the destination is an event or participation in an event.
Idemo na odmor (We are going on holiday). The event is our holiday.
Idem na kavu (I'm going for a coffee). The event is a coffee.
na jedno mjesto 'to one place'
na vrhu on top (at the top)
na kraju in the end
na istom mjestu in the same place
preko ulice across the street
preko puta across the street
Živjela je preko puta. across the street.
preko vikenda over the weekend
Voze prema autobusnom kolodvoru Idemo ravno prema trgu
s mojom kućom with my house kava s mlijekom coffee with milk
S takes the genitive when it refers to a list, so one from something.
s tog albuma from that album.
To recap U is either followed by the accusative or locative case depending on the meaning (and once established that it needs to be used as opposed to na).
U followed by the accusative has the meaning 'to'.
Idem u galeriju I'm going to the gallery
Išli smo u pub We went to the pub
On Monday, on Tuesday etc also uses U followed by a Day of the Week in the accusative.
u ponedjeljak on Monday
u utorak on Tuesday
u parku 'in the park'
u školi 'in school'
u filmovima 'in films'
u restoranima 'in restaurants'
u velikim firmima 'in big firms'
u hotelu 'in the park'
Bili smo u Londonu 'We were in London'
Stanujem u Londonu 'I live in London'
Sada ima kuću u drugom gradu 'Now he has a house in another city'
Za is either followed by the accusative or instrumental depending on the meaning.
za dvije godine for two years
za sve druge for all others
za firmu neće biti dobro it will not be good for the firm
za doručak for breakfast
za stolom behind (at) the table
za drugim stolovima behind (at) other tables
Prepositions taking the Genitive
This bunch, some of whom have been mentioned earlier, all take the genitive.
Od, do, iz, s(a), ispred, iza, izvan, van, unutar, iznad, ispod, prije, poslije, nakon, za, tijekom, tokom, čelo, nakraj, onkraj, krajem, potkraj, sred (nasred, posred, usred), oko, okolo, blizu, kod, kraj, pokraj, pored, i, u, diljem, preko, bez, osim, mjesto (umjesto, namjesto), uime, između, (na)spram, put, protiv, zbog, uslijed.