In hexagonal DyMnO3, Dy(3+) crystal-field excitations are studied as a function of temperature and applied magnetic field. They are complemented with the measurements of infrared active phonon frequency shifts under applied magnetic field at T = 4.2 K. Between TN = 68 K and T = 10 K, the absence of Dy(3+) Kramers doublet splittings at either the C3 or the C3v site symmetries indicates that the Mn(3+) magnetic order effective exchange field has no component parallel to the c-axis at either site. Below T = 10 K, the ground state Kramers doublet splits under the Dy(3+) internal effective field as well as the applied magnetic field. Also, relatively strong infrared active phonon energy shifts are observed in magneto-infrared reflectance measurements at T = 4.2 K, allowing the calculation of the induced electric polarization changes as a function of the applied magnetic field. Such changes are associated with a large magnetoelectric effect in DyMnO3, arising from a charge transfer between Dy(3+) and apical oxygen ions.