There are two ways to get an FBI criminal record check. One is to mail a request to the FBI and receive a criminal record check certificate back by mail.
The other is to submit an application electronically with the FBI or through the FBI approved channellers. This method is faster. The FBI website lists the approved channellers. Please note that criminal record checks from some channellers cannot be opened outside the United States, the services of those channellers can therefore not be used when submitting a criminal record check to the Directorate of Immigration.
In both cases, the applicant needs to be fingerprinted and submit fingerprints with the application. If you are in Iceland, the Reykjavik City Police can take fingerprints.