I think the biggest obstacle will be the fact that you are American (I'm assuming you're American?), as HenryTeach also suggested. Not many schools in the EU recruit non-EU citizens, simply because it is so much easier for them to recruit EU citizens, in terms of paperwork. That is not to say that it is impossible - if you are in Italy and can meet with employers face to face, your chances will improve greatly, although of course there is a financial risk in this. Many Americans, as HenryTeach said, work illegally at first (although I'm not condoning this).
You will certainly need a qualification - the most internationally recognised and accepted are the Cambridge CELTA and Trinity Cert TESOL. These are 120 hour, classroom based courses and include some teaching practice as part of the assessment. There are several other good quality courses of similar length and content too. Generally speaking, the shorter and less classroom-based your course, the more limited your employment options will be.
Try this list of TEFL courses
to find one which suits you.
Hope this helps - good luck!