The most important information in any Finite Element Formulation is the Boundaries and the Boundary Conditions. There are two kinds of boundaries:
Dirichlet Boundaries: On these boundaries, the potential is fixed and known beforehand.
Neumann Boundaries: On these boundaries, the potential is variable and unknown.
A conductor will generally have a fixed potential and hence be a Dirichlet boundary. On the other hand, a dielectric will generally have a Neumann boundary. However, in real life there will be no pure conductors or dielectrics. So it is really dependent on the problem.