Your IDE is your friend. Search for references. The most interesting results will be in "method return type" and "field declaration" as by calling a method with that return type you have an instance and a field will also store an instance. In this case this will reveal the method Minecraft#getEntityRenderDispatcher.
EntityRenderersEvent.AddLayers and use EventPriority.LOWEST so that your handler runs last (after mods have potentially added their custom layers).
EntityRenderDispatcher#renderers and EntityRenderDispatcher#getSkinMap.