I currently work for JET in Japan. They pay great, covered airfare and housing, and they have been very supportive. Are there any similar companies in Italy, Spain, Greece, etc.?
Answer on What are the best ESL companies in Europe?
You'll find that the conditions (and perks) for ESL teaching in Europe are not nearly as good as in some Asian countries like Japan. I'm assuming that you are non-EU based on your other questions, which means you may have a very difficult time finding a work sponsor unless you are well-educated (preferably with a teaching degree, not just ESL) and have extensive experience. It's much easier for employers to hire within the EU (since UK and Ireland can travel freely and there are no special considerations for hiring).
Generally you will need to apply directly with language schools, and don't count on them paying airfare and housing (they won't). If you want to work in the EU, you will usually have to finance it yourself. I have several EU friends that teach ESL in Asia, but find the pay and benefits too low within Europe, and there is so much competition for the jobs. If you want to work in Italy, Spain or Greece, it would help your position to have proficient Italian, Spanish or Greek as well.
Berlitz will hire non-EU for non-EU countries only.