Based on my own experiences, pretty challenging. You have to get a company to sponsor you for a work permit, so you have to have some kind of marketable skill that no one else has. It's especially hard for Americans because citizens from the European Union can all work legally in Italy, so we're really the lowest man on the totem pole.
Some suggestions:
1. See if you can get an American company to hire you to work in the Italian branch of their firm. Many large corporations have branches in Italy.
2. As someone else suggested, try getting a job through the US Armed Forces.
3. Apply to a university or language school in Italy and get a student visa. I think having a student visa allows you to work part time (at least it does here in the States).
4. Work under the table. Yes, it's illegal, but some industries like hotels, restaurants, etc., especially in the larger cities, are looking for people who speak English and are willing to pay them in cash to get around paying taxes/benefits.
Good luck!