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In this paper, we propose a comprehensive framework for performance analysis of multi-hop multi-branch wireless communication systems over Log-Normal fading channels. The framework allows to estimate the performance of Amplify and Forward (AF) relay methods for both Channel State Information (CSI-) assisted relays, and fixed-gain relays. In particular, the contribution of this paper is twofold: i) first of all, by relying on the Gauss Quadrature Rule (GQR) representation of the Moment Generation Function (MGF) for a Log-Normal distribution, we develop accurate formulas for important performance indexes whose accuracy can be estimated a priori and just depends on GQR numerical integration errors; ii) then, in order to simplify the computational burden of the former framework for some system setups, we propose various approximations, which are based on the Improved Schwartz-Yeh (I-SY) method. We show with numerical and simulation results that the proposed approximations provide a good trade-off between accuracy and complexity for both Selection Combining (SC) and Maximal Ratio Combining (MRC) cooperative diversity methods.