Getting Started with GIS has been the most popular Esri web course for several years. It's free and a great learning tool for those brand-new to GIS. You can use ArcGIS for Desktop trial software to complete the course exercises if you don't have access to a paid license.
Hi Suzanne Boden, you may refer to this discussion about Resources for GIS new-comers; how to learn and practice for FREE especially for new comers.
All the best