The lack of available unlicensed spectrum together with the increasing spectrum demand by multimedia applications has resulted in a spectrum scarcity problem, which affects satellite communications (SatCom) as well as terrestrial systems. The goal of this paper is to propose resource allocation (RA) techniques, i.e., carrier, power, and bandwidth allocation, for a cognitive spectrum utilization scenario where the satellite system aims at exploiting the spectrum allocated to terrestrial networks as the incumbent users without imposing harmful interference to them. In particular, we focus on the microwave frequency bands 17.7-19.7 GHz for the cognitive satellite downlink and 27.5-29.5 GHz for the cognitive satellite uplink, although the proposed techniques can be easily extended to other bands. In the first case, assuming that the satellite terminals are equipped with multiple low block noise converters (LNB), we propose a joint beamforming and carrier allocation scheme to enable cognitive space-to-Earth communications in the shared spectrum where fixed service (FS) microwave links have priority of operation. In the second case, however, the cognitive satellite uplink should not cause harmful interference to the incumbent FS system. For the latter, we propose a joint power and carrier allocation (JPCA) strategy followed by a bandwidth allocation scheme, which guarantees protection of the terrestrial FS system while maximizing the satellite total throughput. The proposed cognitive satellite exploitation techniques are validated with numerical simulations considering realistic system parameters. It is shown that the proposed cognitive exploitation framework represents a promising approach for enhancing the throughput of conventional satellite systems.