In many cases, we are interested in finding the ground state of a spin model, that is, the zero temperature, lowest energy state. In many regular models, it is possible to deduce the form of the ground state configurations. However, for disordered frustrated systems, such as spin glasses, finding a ground state is very difficult (in fact it is NP hard --- i.e., there is no polynomial time algorithm for finding a solution).
In practice, ground states are found using simulated annealing. This involves starting from a number of different random initial configurations, and slowly cooling them down to zero temperature. This produces local energy minima that are close to, and possibly equal to, the global minimum.