Well speaking about funerals in general, you can't have ceremonies in church obviously. Those will need to be postponed to when we can go out again.
What you'll have is the bare and simple burial, with a very small group of only close family attending. I know it because my friend's grandma died of stroke a couple days ago and they had a quick burial with only close family attending. They had a priest there say some words.
As for covid-related deaths though, there is more safety measures in place of course. I don't know the specifics but once the body is taken from the hospital I reckon they allow a burial with some family attending maybe? I don't know I'll have to inform myself. I'll get back to you.
Edit: alright apparently if it's a covid-related death the undertakers/funeral parlours need to be in full protective gear and sanitize everything of course, plus very few people can attend the burial. The problem is in the worst hit towns (like Bergamo) they've been having trouble finding room in their graveyards so you either have them wait more for the coffin to be buried or you cremate them. So a lot of covid-19 victims in some northern towns are being cremated.