In general, quality private language schools require a TEFL/ TESOL Certificate (see below). Some method schools do not require this qualification but may require that you follow their own training course, which sometimes means unpaid teaching hours. The pay rates may be below that offered by schools requiring a TEFL qualification.State schools require local pedagogical qualifications, (and they really mean local, it is different in every canton). However, on account of the current lack of qualified teachers in state schools there may be a few openings. It is probably worth contacting the Kantonsschule / Gymnase or Berufsschule / Ecole Professionelle as well as the state supported schools for adult education: the Volkshochschule / Université Populaire in the area you wish to work in. Many state schools of further education will accept a bachelors and masters degree as equivalent to Swiss degrees (Lizenz / licence). They require that you speak the local language, but not necessarily at a very high level.
1. TrainingMost respected TEFL courses provide training in different TEFL/TESOL methodologies. They normally involve about 100+ classroom hours and have a practical training component. The certificates indicated below are recognised by most language schools in Switzerland.
Certificate in English Language Teaching to AdultsThe most well-known worldwide qualification is the Certificate in English Language Teaching to Adults. It is administered by the University of Cambridge Local Examinations Syndicate in the UK. This certificate program is available through language institutes and British Council offices throughout the world. Their website provides information on the CELTA.
For information about CELTA courses in Switzerland, see eslbase.
John Potts has written a paper to explain CELTA in the Swiss context.
Celta in a Swiss context by John Potts (106 KB)
Trinity TESOL certificateLike the CELTA program, Trinity courses are available around the world, and each adheres to a standard syllabus. The certificate is run by Trinity College in London. For more information see their website (Training courses currently unavailable in Switzerland)
International House Certificate in Teaching English as a Foreign LanguageFor more information on the International House Certificate in Teaching English as a Foreign Language (IHCTEFL) please see their website. (Training courses currently unavailable in Switzerland)
SIT TESOL CertificateSIT TESOL Certificate is mostly American-based but a few courses are located outside the USA. For more information please see their website (Training courses currently unavailable in Switzerland)
American & Canadian English in the TEFL industry in SwitzerlandAmerican English is generally absent in private or public schools. But there are some requests for one-to-ones or for TOEFL preparation courses. Berlitz is also just about everywhere in Europe.
Otherwise, if you are agreeable to teaching what is in the British course book, possibly telling students it is different in American English, most schools are more interested in having a qualified and experienced native speaker than in whether they are British or American.