Certificates of IS0 are issued by certification bodies. Examples of well known international certification bodies includes BVQI, DNV etc. The certification body audit the organization and issue a certificate that is accredited by accreditation body. Some of the well known accreditation bodies include RvA- the Dutch accreditation, INMETRO- Brazil etc.
An organization looking for ISO certification has to be prepared by addressing / implementing the standard requirements. Once the implementations of standard requirements are finished, the organization should approach a registrar and establish a contract after which they will conduct external audits and will issue the certificate.
Many training organization also including, training wings provides courses in auditing / assessments and then issue certificates. These certificates are issued by training organization. Good training organizations have accreditation to organizations like UK (International Register of Certificated auditors), RAB in America etc.