A semiclassical approach to the dressed-atom theory is presented in which dressed energies and states are determined from the solutions of the semiclassical coupled equations for the atomic probability amplitudes. The semiclassical approach has an advantage over the standard quantum-mechanical approach especially when an atom interacting with a nonmonochromatic field is considered, because the standard approach requires diagonalization of an infinite-dimensional Hamiltonian matrix for an evalution of dressed energies and states. It is shown that the dressed energies and states, which are obtained semiclassically, are the same as the results calculated quantum-mechanically for a two-level atom driven by a monochromatic and bichromatic field. Explicit expressions for dressed energies and states of a two-level atom interacting with a resonant trichromatic field are given and their degeneracy problems are discussed.