You will need to send certified copies of the death certificate. You will probably need many of them. I think there is some kind of opportunity to get many copies for cheap early on. To get them later on, can cost $5 or more each.
Posting a legal notice in the newspaper is a necessary formality. Most creditors are corporations that don't read local newspapers, but most companies won't cooperate with you unless you have made the legal notice, even if you have sent them a legally certified copy of the death certificate.