Intelligent Reflecting Surfaces (IRS) are a promising solution to enhance the coverage of future wireless networks by tuning low-cost passive reflecting elements (referred to as {metasurfaces}), thereby constructing a favorable wireless propagation environment. Different from prior works, which assume Rayleigh fading channels and do not consider the direct link between a base station and a user, this article develops a framework based on moment generation functions (MGF) to characterize the coverage probability of a user in an IRS-aided wireless systems with generic Nakagami-m fading channels in the presence of direct links. In addition, we demonstrate that the proposed framework is tractable for both finite and asymptotically large values of the metasurfaces. Furthermore, we derive the channel hardening factor as a function of the shape factor of Nakagami-m fading channel and the number of IRS elements. Finally, we derive a closed-form expression to calculate the maximum coverage range of the IRS for given network parameters. Numerical results obtained from Monte-Carlo simulations validate the derived analytical results.