Utilities can be a very confusing subject so I am going to try and give you a good base to work with. Bills normally arrive once every 2 months and you do not send off a check to pay them but instead pay at the post office or have your bank automatically pay them via a bonifico.
FYI Most utility companies do not come out and read the meters. Instead they estimate how much they believe you use and send you a bill for that. This type of bill is called stimata which means estimate. Then, once a year or twice they show up to read the meter and send you an adjusted bill. If they have been estimating low this adjusted bill could be very high. Instead, on your bill you should see someplace where it says something like this:
Basically this says " For the next bill, if we do not come out to read it, we will bill you using the assumption that you have a total of 73928 units on 17 June 2004. If in the 3 days preceding that date you wish to let us know the actual number, please call our toll free number" Normally when you call you are just given a few prompts and you punch in your client number (codice cliente) and the amount of scatti.
You should try to keep on top of this as much as possible.
The company that handles electricity in Italy is ENEL. Electricity in Italy is not like in the US where you can use as much as you need and then just pay every month. Instead, here, you are allotted 3.0 kW. If you use more than this at any one time your power will shut off. That means no running of the washing machine and a hair dryer at the same time. Because of this, looking for appliances with an A or A+ rating* is even more important. You can increase your usage, to 4.5 or 6 which works well but you do pay more per unit of measure. I have 4.5 and am able to run 2 large things plus 2 TVs, 2 refrigerators, a computer, a freezer, a fish tank and lights but if I try to turn on anything else the power will blow. Because we have a water pump (autoclave) we do have to be careful as this consumes a lot and we tend to forget when we have a few things going at once that if we flush or wash our hands the power may go off.
Our gas company here in the province of Siena is Intesa but every area has their own. You should ask your rental agent or real estate agent who to contact for your area. There are different kinds of gas as well. City gas is metano and is pretty reasonable. Most of the bigger towns have this. Even though many towns have it, loads of people never hooked up to the mains so they need to get gas tanks (bombole) to use for cooking etc. My first apt. had this, a gas tank under the sink. Sure I felt really safe! When it runs out you go to the neighborhood store that sells new ones and either bring one home or have them drop one off. When you live outside of where there are gas lines you will need to have a large bombola of gas. They come out and fill these for you but the cost is through the roof (for us it was 9 times what city gas was).
Every area has their own water company. These bills I have noticed only come once or twice a year. Many times if you live in an apartment building and have condominio fees, water will be part of this. As with everything though, keep an eye on the meter. The people who do the accounting for condominiums are not always the brightest bulbs.
To set up a new account you will need to have a legal codice fiscale. You can call and set up most things by phone. When you first get everything set up you will not have residency yet but once you do, let all of the companies know as you get a discount on the rates.