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 percent satisfy f(V)M(V)/f(P)M(P)=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 vertical bar V(cb)vertical bar Cabibbo-Kobayashi-Maskawa matrix element. From the B -> D semileptonic decay we get vertical bar V(cb)vertical bar=0.040 +/- 0.006, in perfect agreement with our previous determination based on the study of the semileptonic Lambda(b)->Lambda(c) 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 g(B*B pi)(0)=60.5 +/- 1.1 and g(D*D pi)(0)=22.1 +/- 0.4. The ratio R=(g(B*B pi)(0)f(B*)root M-D/(g(D*D pi)(0)f(D*)root M-B)=1.105 +/- 0.005 agrees with the heavy quark symmetry prediction of 1.