As you needed to complete forms when you left, you will need to fill in forms when you return. The easiest way is to contact the consulate where you are registered to sort out your situation. You will have to establish a fully detailed inventory of your furniture. A moving form attestation is often demanded when you pass the border (you can ask for it at your Consulate).

You will have to think about school registration if you have children.

Apart from the obvious things that you have to do before moving out of Italy, there is a long list of authorities and other entities that you need to contact to inform them of your departure. You cannot assume (unless assured otherwise) that any one authority, such as your Comune, will notify them on your behalf. These include:

Generally speaking, you can phone a utility and give a final meter reading. You can write to clubs, associations and magazines. You are best to visit the bank and Comune. Other places may require either your physical presence, an autocertification or a letter. Call them to find out. Presumably they will all want to know your new address as well. Leaving rented property is subject to it being left in "good condition"; inspect the property together. If there is a dispute, contact the local branch of SUNIA (Sindacato Unitario Nazionale Inquilini e Assegnatari), the tenants' union (Via S. Luca 12/50, 16124 Genova tel. 010/2476859). Normal wear and tear should be acceptable. 99% of Italians are going to redecorate before they move into a place in any case.