In general, the organization of the exams to obtain the Diploma in Spanish as a Foreign Language (DELE) is run by the Instituto Cervantes. It's webpage contains information regarding the different levels and requiremnts, as well as a list of dates and locations where the exam will be offered.
The scheduling and administration of the exams in the United States is coordinated by the Instituto Cervantes in New York, Chicago, Seattle and Alburquerque, which colaborates with the Education Office of the Embassy of Spain in Washington, D.C.