This paper addresses the problem of fast learning of radar detectors with a limited amount of training data. In current data-driven approaches for radar detection, re-training is generally required when the operating environment changes, incurring large overhead in terms of data collection and training time. In contrast, this paper proposes two novel deep learning-based approaches that enable fast adaptation of detectors based on few data samples from a new environment. The proposed methods integrate prior knowledge regarding previously encountered radar operating environments in two different ways. One approach is based on transfer learning: it first pre-trains a detector such that it works well on data collected in previously observed environments, and then it adapts the pre-trained detector to the specific current environment. The other approach targets explicitly few-shot training via meta-learning: based on data from previous environments, it finds a common initialization that enables fast adaptation to a new environment. Numerical results validate the benefits of the proposed two approaches compared with the conventional method based on training with no prior knowledge. Furthermore, the meta-learning-based detector outperforms the transfer learning-based detector when the clutter is Gaussian.