The main desktop software suppliers ESRI (ArcGIS), Pitney Bowes(MapInfo) and Quantum GIS have many resources on-line which can be easily accessed to help in the task of learning about GIS software functionality. However, if you have a specific problem to solve and limited time scales to achieve it you may decide to take either an on-line course or an intensive one or two day course from a GIS trainer.
On-line courses are now very sophisticated and can be interactive. These types of courses may answer your requirements especially if you are not able to find a suitable training course within easy travel distance from your location. Both on-line and on-site have advantages and disadvantages which could be the subject for another day. As previously mentioned I do not believe that there is a specific solution which meets everyone's needs. In the final analysis your specific criteria will dictate what will be the best solution to your requirements.