I'm new to ArcGIS API for Javscript V3, and trying to dynamically create group layers and add layers together in a existing layer list. I'm not sure how to get this done.
There isn't any sort of capability in 3.x to provide group layers. This is why ArcGIS Online web maps currently cannot support group layers. The GroupLayer class was introduced in the 4.x API.
The only way to have group layers in 3.x is to use map services that are already configured with group layers.