This paper studies the wireless spectrum sharing between a pair of distributed primary radio (PR) and cognitive radio (CR) links. Assuming that the PR link adapts its transmit power and/or rate upon receiving an interference signal from the CR and such transmit adaptations are observable by the CR, this results in a new form of feedback from the PR to CR, refereed to as hidden PR feedback, whereby the CR learns the PR's strategy for transmit adaptations without the need of a dedicated feedback channel from the PR. In this paper, we exploit the hidden PR feedback to design new learning and transmission schemes for spectrum sharing based CRs, namely active learning and supervised transmission. For active learning, the CR initiatively sends a probing signal to interfere with the PR, and from the observed PR transmit adaptations the CR estimates the channel gain from its transmitter to the PR receiver, which is essential for the CR to control its interference to the PR during the subsequent data transmission. This paper proposes a new transmission protocol for the CR to implement the active learning and the solutions to deal with various practical issues for implementation, such as time synchronization, rate estimation granularity, power measurement noise, and channel variation. Furthermore, with the acquired knowledge from active learning, the CR designs a supervised data transmission by effectively controlling the interference powers both to and from the PR, so as to achieve the optimum performance tradeoffs for the PR and CR links. Numerical results are provided to evaluate the effectiveness of the proposed schemes for CRs under different system setups.