These links will help you get started with ArcGIS. The Libraries offer workshops and individual consultations. There are courses are available through the Office of Continuing Education of the New Jersey Agricultural Experiment Station (for a fee).
Official ESRI ArcGIS Training Resources
A regularly updated collection of ArcGIS trainings offered online. ESRI provides both video and traditional tutorial guides as well as MOOCs and web courses. The topics range in complexity, from those designed for beginners for the suite of applications, to more advanced subjects like analytics, data management, python scripting, creating web-based geo-applications and StoryMaps.
GIS Dictionary
Defines all acronyms and terminology used in ESRI ArcGIS applications as well as other GISs. It is a useful tool for learning standard GIS terminology.
GeoDeltaLabs
A youtube channel with instructional videos covering ArcGIS, Google Earth, QGIS and other GIS related topics.
Harvard University's GIS Videos
Recordings of workshops at Harvard's Center for Geographic Analysis.
iSchool@Syracuse Article
This article offers information about some of the basic concepts of GIS and how librarians can help with your GIS data.