Priests have been, throughout history, the only ones who can perform exorcisms. They might get a thorough education, but until recently, Catholic exorcists (who make up the majority of exorcists worldwide) underwent very little formal training.
In the early 1990s, however, exorcism training became more standardized when the International Catholic Association of Exorcists (ICAE) formed. Members get quarterly newsletters and meetings in Rome twice a year. In 2005, the Regina Apostolorum Pontifical Apostolorum began to offer an official course on exorcism.
The American Association of Exorcists, founded in 2003, offers examinations and certifications, and don't forget that Reverend Bob Larson who offers exorcism seminars for those hoping to get fightin' those demons as soon as humanly possible.