I am going to a funeral this afternoon and hoping someone can help me with what to say in Italian. I know that in Ireland at the end of the mass everyone files past the family and (unless they are very close to the family, which I am not in this case) says 'Sorry for your loss'. Will the same thing be done here, and if so, what is the equivalent in Italian?

Thanks

Italian funerals are usually divided in four parts: first all the participants meet by the decesed's house (or at the hospital). Relatives and close friends can go to the aparrtment to meet the family and offer the "condoglianze". (Just say "condoglianze" or add anything that you think conveys your feelings.) The other wait for the family and coffing to appear and say "Condoglianze" on the street. Than the group of people walk to the church (most usually); some town have a specific place where the nonreligious can have a service, but if the death or his or her family opted for a civil funeral, mostly the service will be held in front of the house or in a place that's meaningful for the deceased: political party office, place where he or she worked as a volunteer or similar. After the cerimony you may have another occasion to shake hands and express your "condoglianze", but you may notice that some people leave the funeral right after reaching the church, because the meaningful part to many is the parading of the coffin, not the function. Finally, family and maybe close friends will accompany the coffin to the graveyard where it will be buried or, increasingly often, be awaiting for incineration.

A few months ago I had to give condolences but I didn't know what to say, then more recently I was sadly on the recieving end of the 'condoglianze'. I found that people didn't exactly say 'condoglianze' to me but I remember one said 'mi dispiace' and others conveyed their sympathies in their own words like Alice said.

condoglianze is the standard word, then of course you can add a variant or say "ti sono vicino", "mi dispiace" and similar.
It depends on how close you are to the family.
You don't say to your grand-ma "condoglianze" if your grand-pa is dead.

Condoglianze = con + dolenza = with grief
Any equivalent is fine. I would never bother to say something if I don't know well the family of the dead person (altough I might know him/her well)

When my father died my neighbor said- Mi dispiace che tu hai perso il tuo padre.

I felt much better, hearing that. It seemed almost as if I had found a new family here.