This paper considers a multiple-input multiple-output system with low-resolution analog-to-digital converters (ADCs). In this system, we propose a novel communication framework that is inspired by supervised learning. The key idea of the proposed framework is to learn the nonlinear input-output system, formed by the concatenation of a wireless channel and a quantization function used at the ADCs for data detection. In this framework, a conventional channel estimation process is replaced by a system learning process, in which the conditional probability mass functions (PMFs) of the nonlinear system are empirically learned by sending the repetitions of all possible data signals as pilot signals. Then, the subsequent data detection process is performed based on the empirical conditional PMFs obtained during the system learning. To reduce both the training overhead and the detection complexity, we also develop a supervised-learning-aided successive-interference-cancellation method. In this method, a data signal vector is divided into two subvectors with reduced dimensions. Then, these two subvectors are successively detected based on the conditional PMFs that are learned using artificial noise signals and an estimated channel. For the case of 1-bit ADCs, we derive an analytical expression for the vector error rate of the proposed framework under perfect channel knowledge at the receiver. Simulations demonstrate the detection error reduction of the proposed framework compared to conventional detection techniques that are based on channel estimation.