This paper presents a study about methods for normalization of historical texts. The aim of these methods is learning relations between historical and contemporary word forms. We have compiled training and test corpora for different languages and scenarios, and we have tried to read the results related to the features of the corpora and languages. Our proposed method, based on weighted finite-state transducers, is compared to previously published ones. Our method learns to map phonological changes using a noisy channel model; it is a simple solution that can use a limited amount of supervision in order to achieve adequate performance. The compiled corpora are ready to be used for other researchers in order to compare results. Concerning the amount of supervision for the task, we investigate how the size of training corpus affects the results and identify some interesting factors to anticipate the difficulty of the task.