This paper presents the design, implementation, and results from a dynamic wireless spectrum access system built using GNU Radio and software-defined radios (SDRs) as part of an undergraduate senior design project. The project involved designing and implementing a dynamic wireless spectrum access system in which the secondary user (SU) learns the unknown transmission behavior (channel occupancy and time slots) of the primary user (PU) and then opportunistically transmits during time slots and using channels when they are not being used by the PUs. The main design objective was to maximize the throughput of the SU while minimizing the interference to the PU. A transmitted signal energy detection algorithm with an adaptive threshold was employed to set the channel states as occupied or not occupied. Channel state information was used to determine the PU behavior in a deterministic manner such that the unused time slots and channels could be exploited. A channel allocation scheme for the SU is proposed using the PU channel occupancy information to calculate the channel(s) and time slots available to the SU at any given time. Simulation and physical testing of the system validate the proposed algorithms. Students' feedback affirms GNU Radio and SDRs to be an effective platform for introducing abstract mathematical communications theory concepts, such as cognitive radios and dynamic spectrum allocation, in a hands-on manner.