  We describe in detail two numerical simulation methods valid to study systems
whose thermostatistics is described by generalized entropies, such as Tsallis.
The methods are useful for applications to non-trivial interacting systems with
a large number of degrees of freedom, and both short-range and long-range
interactions. The first method is quite general and it is based on the
numerical evaluation of the density of states with a given energy. The second
method is more specific for Tsallis thermostatistics and it is based on a
standard Monte Carlo Metropolis algorithm along with a numerical integration
procedure. We show here that both methods are robust and efficient. We present
results of the application of the methods to the one-dimensional Ising model
both in a short-range case and in a long-range (non-extensive) case. We show
that the thermodynamic potentials for different values of the system size N and
different values of the non-extensivity parameter q can be described by scaling
relations which are an extension of the ones holding for the Boltzmann-Gibbs
statistics (q=1). Finally, we discuss the differences in using standard or
non-standard mean value definitions in the Tsallis thermostatistics formalism
and present a microcanonical ensemble calculation approach of the averages.
