  A new ``Dynamical Mean-field theory'' based approach for the Kondo lattice
model with quantum spins is introduced. The inspection of exactly solvable
limiting cases and several known approximation methods, namely the second-order
perturbation theory, the self-consistent CPA and finally a moment-conserving
decoupling of the equations of motion help in evaluating the new approach. This
comprehensive investigation gives some certainty to our results: Whereas our
method is somewhat limited in the investigation of the J<0-model, the results
for J>0 reveal important aspects of the physics of the model: The energetically
lowest states are not completely spin-polarized.A band splitting, which occurs
already for relatively low interaction strengths, can be related to distinct
elementary excitations, namely magnon emission (absorption) and the formation
of magnetic polarons. We demonstrate the properties of the ferromagnetic Kondo
lattice model in terms of spectral densities and quasiparticle densities of
states.
