The Astroneu array consists of three autonomous Extensive Air Shower (EAS) detection stations installed and operated at the Hellenic Open University campus. Each station (Astroneu station) combines two different detection technologies. Three charged particle detectors arranged in a triangle and an RF antenna in the middle. Before installation several calibration procedures were performed both to the individual detectors of the array as well as to each integrated Astroneu station. In this paper we present the development of simulation methods, data analysis techniques and experimental procedures, which have been used to calibrate and optimize the operating parameters of the Astroneu particle detectors, to process the experimental signals and extract timing and amplitude information, to correct for systematic biases and estimate precisely the particle-front arrival time on each individual detector resulting to accurate reconstruction of the detected EAS direction. Furthermore, the performance of the Astroneu telescope in detecting and reconstructing EAS is demonstrated with special inter-calibration runs, where pairs of stations are detecting simultaneously the same air shower, as well as with comparisons against the predictions of a detailed simulation description of the detectors.