The low frequency array (LOFAR), is the first radio telescope designed with the capability to measure radio emission from cosmic-ray induced air showers in parallel with interferometric observations. In the first 2 years of observing, 405 cosmic-ray events in the energy range of 1016??1018 eV have been detected in the band from 30??80 MHz. Each of these air showers is registered with up to 1000 independent antennas resulting in measurements of the radio emission with unprecedented detail. This article describes the dataset, as well as the analysis pipeline, and serves as a reference for future papers based on these data. All steps necessary to achieve a full reconstruction of the electric field at every antenna position are explained, ...