  We study Monte Carlo calculations of the effective potential for a scalar
field theory using three techniques. One of these is a new method proposed and
tested for the first time. In each case we extract the renormalised quantities
of the theory. The system studied in our calculations is a one component
$\phi^4$ model in two dimensions. We apply these methods to both the weak and
strong coupling regime. In the weak coupling regime we compare our results for
the renormalised quantities with those obtained from two-loop lattice
perturbation theory. Our results are verified in the strong coupling regime
through comparison with the strong coupling expansion. We conclude that
effective potential methods, when suitably chosen, can be accurate tools in
calculations of the renormalised parameters of scalar field theories.
