The Zwicky Transient Facility (ZTF) has been observing the entire northern sky since the start of 2018 down to a magnitude of 20.5 ($5 sigma$ for 30s exposure) in $g$, $r$, and $i$ filters. Over the course of two years, ZTF has obtained light curves of more than a billion sources, each with 50-1000 epochs per light curve in $g$ and $r$, and fewer in $i$. To be able to use the information contained in the light curves of variable sources for new scientific discoveries, an efficient and flexible framework is needed to classify them. In this paper, we introduce the methods and infrastructure which will be used to classify all ZTF light curves. Our approach aims to be flexible and modular and allows the use of a dynamical classification scheme and labels, continuously evolving training sets, and the use of different machine learning classifier types and architectures. With this setup, we are able to continuously update and improve the classification of ZTF light curves as new data becomes available, training samples are updated, and new classes need to be incorporated.