How do electric charges exert forces?
An electric charge creates an electrical environment around it which we call an electric field. This field interacts with the other charges present in the region and exert forces. Thus, the interaction can be described as a two step process, creation of the field and interaction of the field with the charges,
The field is not just and artifact, but has a physical role and can as well transfer energy and momentum. It is not established instantly but, takes a finite time to propagate (at the speed of light).