There are several major bodies of international accreditation - including U.S.-based accreditation as well as IB (International Baccalaureate) World Schools. The schools typically go through a rigourous process to achieve these qualifications and must keep them updated regularly.
Registered International schools are sometimes only allowed to accept students with a citizenship outside the host country.
Kindergartens and pre-schools may exist in the gray area - not official international schools and also not official local kindergartens. It's worth checking closely as they may only hold a training license.