EPICS Training courses have been run by various organizations at various times as the demand arises. The US Particle Accelerator School used to organize an introductory course every 2-3 years, but has not asked the previous lecturers to run one recently.
The following commercial companies may be able to run EPICS training courses tailored to specific needs, for a fee:
The following are links to the training materials available online that I know about.
The Software Services group at APS ran a 6-month series of courses aimed at local users, with most of the lectures being recorded on video. The talks given in 2014 are here and the 2015 lectures are here.
The USPAS ran an EPICS course in Albuquerque NM from June 23-27, 2014. The lectures and exercises used on this course will be published here.
A series of training days are being held at the APS for new staff over the Summer of 2013. The slides and other materials are here.
A short beginning EPICS course was held at the APS in January 2011, the slides can be found here.
The Controls group at SLAC has run a fairly active EPICS training schedule in recent years. Quicktime movies are available for several of these lectures, for example this Asyn and areaDetector course:
The USPAS organized an EPICS course in Boston Massachusetts from June 14-18, 2010. The lectures used on this course are available here.
The Swiss Light Source have made their EPICS training materials available. As part of this, they have put together a course on writing Channel Access client applications in C which looks very useful for an experienced C programmer starting out with EPICS (it would be a good idea to have a local expert configure the lessons for your site before giving it to someone to use though).
The USPAS organized an EPICS course in Houston, Texas from January 15-19, 2007. The lectures used on this course are available here.
SNS held a training course in October 2006; their slides and other materials are available here.
The January 2005 USPAS in San Francisco included a 1-week EPICS course. Some time I may get around to putting these lectures online...
The ASD/Controls and AOD/BCDA groups at Argonne National Laboratory coordinated a series of lectures entitled "Getting Started with EPICS" in 2004-2005. The lectures were grouped in sessions targeted towards those interested in using EPICS tools, those interested in developing EPICS-enabled programs, and those interested in working with EPICS Input/Output Controller (IOC) software.
All of the lectures were videotaped and are available as streaming video from the Lecture Series webpage.
The 2003 USPAS at Baton Rouge, Louisianna included a 2-week EPICS course which was also the first course to use Linux IOCs running R3.14.1. The slides for this are here (you will need OpenOffice to view some of these lectures).
The 1999 USPAS was based at Argonne, and included a 1-week EPICS course with R3.13 IOCs running vxWorks provided by the Accelerator Systems Division controls group. The slides for this are here (you will need MS PowerPoint to view these lectures).
Several labs have arranged for on-site training courses from Observatory Sciences Ltd. These have been mostly based on the other materials linked here, but there are some additional lectures available from their EPICS page.
The EPICS group at LANL used to run 1-week courses teaching application development, but no longer do so. Their old Training Slides are here.