In this work a numerical approach for the determination of the energy spectra and the calculation of thermodynamic properties of magnetic molecules is presented. The work is focused on the treatment of spin systems which exhibit point-group symmetries. Ring-like and archimedean-type structures are discussed as prominent examples. In each case the underlying spin quantum system is modeled by an isotropic Heisenberg Hamiltonian. Its energy spectrum is calculated either by numerical exact diagonalization or by an approximate diagonalization method introduced here. In order to implement full spin-rotational symmetry the numerical approach at hand is based on the use of irreducible tensor operators. Furthermore, it is shown how an unrestricted use of point-group symmetries in combination with the use of irreducible tensor operators leads to a reduction of the dimensionalities as well as to additional information about the physics of the systems. By exemplarily demonstrating how the theoretical foundations of the irreducible tensor operator technique can be realized within small spin systems the technical aspect of this work is covered. These considerations form the basis of the computational realization that was implemented and used in order to get insight into the investigated systems.