On one hand, we investigated the decay rates of meson decays from the basic computations of the Feynman diagrams. Under this approach, we derived analytically expressions for the square amplitudes of leptonic and semileptonic decays and finally used them to determine the analytical and numerical results for the decay rates. With decay rates results at our disposal, we determined the branching ratios of leptonic and semileptonic decays separately within the standard model (SM) compared our results to the latest theoretical and experimental results. On the other hand, we focused on the effective Lagrangian (EL) under weak interaction from a general approach and used it in our calculation of differential decay rates of mesons. Thereafter, we calculated the total decay rates via integration with respect to. In addition, using the total decay rates results, the branching ratios and the contributions from the new physics (NP) operators were investigated resulting in some phenomenologies of physics beyond the SM.