  Instanton processes are present in a variety of quantum field theories
relevant to high energy as well as condensed matter physics. While they have
led to important theoretical insights and physical applications, their
underlying features often remain elusive due to the complicated computational
treatment. Here, we address this problem by studying topological as well as
non-topological instantons using Monte Carlo methods on lattices of interacting
spins. As a proof of principle, we systematically construct instanton solutions
in $O(3)$ non-linear sigma models with a Dzyaloshinskii-Moriya interaction in
$(1 + 1)$ and $(1 + 2)$ dimensions, thereby resembling an example of a chiral
magnet. We demonstrate that, due to their close correspondence, Monte Carlo
techniques in spin-lattice systems are well suited to describe topologically
non-trivial field configurations in these theories. In particular, by means of
simulated annealing, we demonstrate how to obtain domain walls, merons and
critical instanton solutions.
