This paper presents a detailed framework for adaptive low-complexity and power-efficient resource allocation in decentralized device-to-device (D2D) networks. The adopted system model considers that active devices can directly communicate via specified signaling channels. Each D2D receiver attempts to allocate its D2D resources by selecting a D2D transmitter and one of its spectral channels that can meet its performance target. The process is performed adaptively over successive packet durations with the objective of limiting the transmit power on D2D links while reducing the processing complexity. The proposed D2D link adaptation scheme is modeled and analyzed under generalized channel conditions. It considers the random impact of potential D2D transmitters as well as the random number of co-channel interference sources on each D2D link. Interference cancelation schemes are also addressed to alleviate co-channel interference, which can ease the D2D resource allocation process. Generalized formulations for the statistics of the resulting signal-to-interference plus noise ratio (SINR) of the proposed adaptation scheme are presented. Moreover, generic analytical results were developed for some important performance measures as well as processing load measures. They facilitate tradeoff studies between the achieved performance and the processing complexity of the proposed scheme. Insightful results for the distributions of SINRs on individual D2D links under specific fading models are shown in this paper. The results herein add enhancements to some previous contributions and can handle various practical constraints.