After you have decided to teach English in Europe should be to decide what country you'd like to teach in. it may be quite a difficult task for you, so a lot of research work should be applied.
Every European country has certain requirements to the people willing to be English teachers there, and it's much easier to find a job in some countries than it is in others. For example:
Germany has a big demand for native English speakers, and getting a residency permit for teaching English in Germany is quite not difficult thing. You do need TEFL certification and a secured job before you can receive a work permit.
France is a place where a lot of teachers with TEFL certificate like to come, and job competition is fairly tough. Surprisingly, knowledge of business will get you further in your job search in France than a good command of language. The majority of teachers are hired not to schools and universities but at companies and firms, and the more you know about international communication the easier it will be to find a job. Good business English will help be beneficial.
Greece is a country hard to employ, because visa requirements and red tape can be rather complicated to settle. You won't find many TEFL teachers in Greece because the permits to work are so hard to obtain.
Italy. Its even more difficult to penetrate here that to Greece. Only if you have a passport of a EU citizen. American residents are rarely have a chance to be hired, and if they are it must be prove that it is worth so. Few companies and schools are willing to hire Americans because the process can be costly and time consuming.
Mention that the country you are going to teach English in should be chosen very carefully. It might be the country you just eager to live and stay in, the major factor might be the opportunity of finding a job. Unless you have a job lead already, you must be prepared to do a great deal of search before finding the one.