Qualification requirements vary, depending on the organisation in question. In all cases preference is given to native English speakers.
Independent schools usually want university-educated teachers, qualified in their specific subject.
Language academies vary in their requirements. Some are looking for native English teachers with a TEFL certificate. Others require a language degree, usually in English but also Spanish, French, German or Italian. Some academies accept teachers with no teaching experience, others require at least some previous work in the profession.
After-school classes are held in primary schools. The schools are generally happy to accept a native English speaker with enthusiasm and a desire to help young learners improve. A TEFL certificate is essential.