This thesis focuses on the development of multiuser access schemes for spectrum sharing systems whereby secondary users that are randomly positioned over the coverage area are allowed to share the spectrum with primary users under the condition that the interference observed at the primary receiver is below a predetermined threshold. In particular, two scheduling schemes are proposed for selecting a user among those that satisfy the interference constraints and achieve an acceptable signal-to-noise ratio level above a predetermined signal-to-noise threshold at the secondary base station. The first scheme selects the user that reports the best channel quality. In order to alleviate the high feedback load required by the first scheme, a second scheme is proposed that is based on the concept of switched diversity where the base station scans the users in a sequential manner until an acceptable user is found. In addition, the proposed scheduling schemes operate under two power adaptive settings at the secondary users that are based on the amount of interference available at the secondary transmitter. In the On/Off power setting, users are allowed to transmit based on whether the interference constraint is met or not, while in the full power adaptive setting, users are allowed to vary their transmission power to satisfy the interference constraint. A special case of the proposed schemes is also analyzed whereby all the users are assumed to be at the same position, thus operating under the influence of independent and identically distributed Rayleigh fading channels. Finally, several numerical results are illustrated for the proposed algorithms where the trade-off between the average spectral efficiency and average feedback load of both schemes are shown.