The Italian prepositions are: di (of), a (at, to), da (from), in (in, to, into), con (with), su (on, over, on top of), per (for), tra/fra (between).
The prepositions di, a, da, in, and su always contract with the article to form a single word. The preposition con occasionally contracts; the preposition per contracted in old Italian and it rarely does nowadays.
When to use which preposition is difficult; even after years of studying Italian you will occasionally slip. So, don't obsess about it, use what makes most sense, read a lot of Italian so you can get a feel for the use of prepositions and they will eventually just come. Also, note and learn the following uses of prepositions:
alle 9, alle 10, a mezzanotte, a mezzogiorno (at 9, at 10, at midnight, at noon)
in Italia, in Francia, in America, in California (in, with feminine singular countries)
nel Messico, negli Stati Uniti, nel Giappone, nelle Filippine (in+article, with masculine or plural countries)
a Roma, a Burlington, a Berlino, a Parigi, a Winooski (a, with cities/towns)
in aereo, in macchina, in bicicletta, in treno
a teatro, al cinema