I really only know about SE Asia and doing the TESL/TEFL thing. I'm not sure about Europe. It just depends on how exactly you're going to be doing this - if you're looking for an actual job teaching English, a BA/BS and some sort of ESL certification would probably be required.
What you could do is place an ad in the paper offering to teach English. Again, not sure if it's the same in Europe, but you usually see more money if you do it independently, then things such as visas (not like you'll need to worry about it if you have your It. citi) won't be as much as an issue. Also, since it won't be required for paperwork, having an ESL certification would probably be more for the family than anything else.
You can also look through universities to see if you can get set up with a job. When my brother studied in Lyon for a year, he taught English on the side (no certifications or anything).
There are tons of sites with information regarding the difference certifications and different costs/methods of teaching. You may just want to look that one up since it's easy to find and you're the one that knows what area you're looking at, etc.
Good luck.