We present experimental results and theoretical methods for the precise determination of the presence and the number of persons in an observed area by using Wi-Fi signals. Our setup does not require active cooperation of persons present in the Wi-Fi field, and relies only on the Received Signal Strength Indicator (RSSI), which is read by the detectors. We first show that the standard deviation of the measured RSSI data can be used as a practical tool to establish the presence of a person (or more persons) with high precision, in particular when the signal source is inside the measurement room. For the more difficult problem of counting the number of persons, we have employed machine learning algorithms to analyze data collected on nine different detectors and up to nine people present in our experiment. We have achieved excellent results (prediction accuracy of $98 \%$ and above) for counting already with only few detectors utilized in the analysis. While generalizations to nontrivial indoor geometries (such as odd shapes, more rooms, and greater size) may be of interest in some applications, where additional care with respect to positioning od detectors can be needed (or even placing additional detectors), this approach may be useful due to its conceptual practicality and solid prediction results.