In this paper, the non-orthogonal multiple access technology is integrated into cognitive orthogonal frequency division multiplexing (OFDM) systems, referred to as NOMA-OFDM, to boost the system capacity as well as the number of accessible users. The considered problem is formulated as jointly optimizing the sensing duration, user selection, and power allocation under the constraints of maximum transmitted power and maximum allowable interference. In order to overcome the non- convexity, we decompose the formulated problem into three subproblems, i.e., the sensing duration optimization, user selection optimization and power allocation optimization. By exploiting the individual characteristic of each subproblem, three efficient algorithms, i.e., bisection search method, matching-theory-based user selection and difference of convex (DC) programming, are proposed to solve the corresponding subproblems, respectively. Moreover, an alternate iteration algorithm is also provided to perform joint optimization of three subproblems. Simulation results validate the fast convergence and considerable performance gain of the proposed algorithms.