An efficient method for generating correlated Nakagami-m fading envelope samples is presented; this method is applicable for arbitrary values of the fading parameter m. The new method is compared to other methods used to generate Nakagami-m random variates. An accurate approximation to the inverse Nakagami-m cumulative distribution function, valid for all values of m, is derived. Uncertainties regarding the autocorrelation of the Nakagami-m fading process are discussed. The fading envelope autocorrelation is determined by simulation and asymptotic analysis.