We investigate the problem of distributed channel selection using a game-theoretic stochastic learning solution in an opportunistic spectrum access (OSA) system where the channel availability statistics and the number of the secondary users are apriori unknown. We formulate the channel selection problem as a game which is proved to be an exact potential game. However, due to the lack of information about other users and the restriction that the spectrum is time-varying with unknown availability statistics, the task of achieving Nash equilibrium (NE) points of the game is challenging. Firstly, we propose a genie-aided algorithm to achieve the NE points under the assumption of perfect environment knowledge. Based on this, we investigate the achievable performance of the game in terms of system throughput and fairness. Then, we propose a stochastic learning automata (SLA) based channel selection algorithm, with which the secondary users learn from their individual action-reward history and adjust their behaviors towards a NE point. The proposed learning algorithm neither requires information exchange, nor needs prior information about the channel availability statistics and the number of secondary users. Simulation results show that the SLA based learning algorithm achieves high system throughput with good fairness.