  We illustrate the mass and charge renormalization procedures in quantum field
theory using, as an example, a simple model of interacting electrons and
photons. It is shown how addition of infinite renormalization counterterms to
the Hamiltonian helps to obtain finite and accurate results for the S-matrix.
In order to remove the ultraviolet divergences from the Hamiltonian, we apply
the Greenberg-Schweber ``dressing transformation'' and the Glazek-Wilson
``similarity renormalization''. The resulting ``dressed particle'' Hamiltonian
is finite in all orders of the perturbation theory and yields accurate S-matrix
and bound state energies. The bare and virtual particles are removed from the
theory, and physical dressed particles interact via direct
action-at-a-distance.
