One of the key properties of single-photon detectors is their recovery time, i.e. the time required for the detector to recover its nominal efficiency. In the case of superconducting nanowire single-photon detectors (SNSPDs), which can feature extremely short recovery times in free-running mode, a precise characterization of this recovery time and its time dynamics is essential for many quantum optics or quantum communication experiments. We introduce a fast and simple method to characterize precisely the recovery time of SNSPDs. It provides full information about the recovery of the efficiency in time for a single or several consecutive detections. We also show how the method can be used to gain insight into the behavior of the bias current inside the nanowire after a detection, which allows predicting the behavior of the detector and its efficiency in any practical experiment using these detectors.