The prediction of links among variables from a given dataset is a task referred to as network inference or reverse engineering. It is an open problem in bioinformatics and systems biology, as well as in other areas of science. Information theory, which uses concepts such as mutual information, provides a rigorous framework for addressing it. While a number of information-theoretic methods are already available, most of them focus on a particular type of problem, introducing assumptions that limit their generality. Furthermore, many of these methods lack a publicly available implementation. Here we present MIDER, a method for inferring network structures with information theoretic concepts. It consists of two steps: first, it provides a representation of the network in which the distance among nodes indicates their statistical closeness. Second, it refines the prediction of the existing links to distinguish between direct and indirect interactions and to assign directionality. The method accepts as input time-series data related to some quantitative features of the network nodes (such as e.g. concentrations, if the nodes are chemical species). It takes into account time delays between variables, and allows choosing among several definitions and normalizations of mutual information. It is general purpose: it may be applied to any type of network, cellular or otherwise. A Matlab implementation including source code and data is freely available (http://www.iim.csic.es/~gingproc/mider.html). The performance of MIDER has been evaluated on seven different benchmark problems that cover the main types of cellular networks, including metabolic, gene regulatory, and signaling. Comparisons with state of the art information-theoretic methods have demonstrated the competitive performance of MIDER, as well as its versatility. Its use does not demand any a priori knowledge from the user; the default settings and the adaptive nature of the method provide good results for a wide range of problems without requiring tuning.