In this paper, we develop multiuser access schemes for spectrum sharing systems whereby secondary users 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, we devise two schemes for selecting a user among those that satisfy the interference constraint and achieve an acceptable signal-to-noise ratio level. The first scheme selects the user that reports the best channel quality. In order to alleviate the high feedback load associated with the first scheme, we develop a second scheme 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 to these two selection schemes, we consider two power adaptive settings at the secondary users 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, the users are allowed to vary their transmission power to satisfy the interference constraint. Finally, we present numerical results for our proposed algorithms where we show the trade-off between the average spectral efficiency and average feedback load for both schemes.