We present a method for the simultaneous estimation of the basic reproductive number, R(0), and the serial interval for infectious disease epidemics, using readily available surveillance data. These estimates can be obtained in real time to inform an appropriate public health response to the outbreak. We show how this methodology, in its most simple case, is related to a branching process and describe similarities between the two that allow us to draw parallels which enable us to understand some of the theoretical properties of our estimators. We provide simulation results that illustrate the efficacy of the method for estimating R(0) and the serial interval in real time. Finally, we implement our proposed method with data from three infectious disease outbreaks.