We present results for different observables in weak decays of pseudoscalar and vector mesons with a heavy c or b quark. The calculations are done in a nonrelativistic constituent quark model improved at some instances by heavy quark effective theory constraints. We determine pseudoscalar and vector meson decay constants that within a few per cent satisfy fV MV /fP MP = 1, a result expected in heavy quark symmetry when the heavy quark masses tend to infinity. We also analyze the semileptonic B → D and B → D * decays for which we evaluate the different form factors. Here we impose heavy quark effective theory constraints among form factors that are not satisfied by a direct quark model calculation. The value of the form factors at zero recoil allows us to determine, by comparison with experimental data, the value of the |V cb | Cabbibo-KobayashiMaskawa matrix element. From the B → D semileptonic decay we get |V cb | = 0.040 ± 0.006 in perfect agreement with our previous determination based on the study of the semileptonic Λ b → Λc decay and also in excellent agreement with a recent experimental determination by the DELPHI Collaboration. We further make use of the partial conservation of axial current hypothesis to determine the strong coupling constants gB * Bπ(0) = 60.5 ± 1.1 and gD * Dπ(0) = 22.1 ± 0.4. The ratio R = ( gB * Bπ(0) fB * √ MD )/( gD * Dπ(0) fD * √ MB ) = 1.105 ± 0.005 agrees with the heavy quark symmetry prediction of 1.