I've heard many different pronuciations for "Fianchetto," but which is the proper way to say it? The different pronuciations stem around the "ch" in the middle of the word. Is this said with a hard "k" sound? A soft "sh" sound (as in, sheet)? A "ch" sound, as in church?

Also, what language does this word belong to? We know that it describes a position of the bishop in a chess game, but what does the word actually mean?

It is a hard "k" sound. It is Italian and it means little flanking.

http://www.chess.com/forum/view/general/how-do-you-pronounce-fianchetto?lc=1

it is like this (piano) move out the p make it F and move out the O so u make now the 1st fian ,now the (che) like this its not hard because it is E at the end so it sounds like check move out the CK so it is che ,,,now SAY IT FIAN---CHE---TTO maybe it helps hehehehhe 

http://education.yahoo.com/reference/dictionary/entry/fianchetto

FEE-AN-KET-OH The "ch" in Italian is pronounced with a hard c sound unless it's preceded be an i or e.