The most straightforward method to simulate fast switching in magnetic systems is the solution of stochastic equations of motion for magnetic moments (Langevin dynamics), where thermal fluctuations are taken into account by the thermal (random) field Hfl. In this paper, we address first an important methodical problem of this formalism: the choice of the stochastic calculus (Ito or Stratonovich). We prove that both Ito and Stratonovich stochastic integrals give identical results, despite the multiplicative noise present in the stochastic Landau-Lifshitz-Gilbert equation. Discussing correlation properties of Hfl (which is usually assumed to be δ correlated both in space and time), we point out that finite correlation time and radius of this field can be due not only to physical reasons (heat-bath correlations), but can also arise from the finite-element representation of the continuous problem. Afterwards, we present simulation results concerning the influence of thermal fluctuations on the fast switching of magnetic nanoelements. We consider three typical situations: (1) thermal noise influence on the switching which would happen also in the absence of thermal fluctuations (thermally assisted switching); (2) thermally induced switching of the metastable states; and (3) changing of the switching mode as the consequence of thermal fluctuations.