This paper develops novel deep learning-based architectures and design methodologies for an orthogonal frequency division multiplexing (OFDM) receiver under the constraint of one-bit complex quantization. Single bit quantization greatly reduces complexity and power consumption, but makes accurate channel estimation and data detection difficult. This is particularly true for multicarrier waveforms, which have high peak-to-average ratio in the time domain and fragile subcarrier orthogonality in the frequency domain. The severe distortion for one-bit quantization typically results in an error floor even at moderately low signal-to-noise-ratio (SNR) such as 5 dB. For channel estimation (using pilots), we design a novel generative supervised deep neural network (DNN) that can be trained with a reasonable number of pilots. After channel estimation, a neural network-based receiver -- specifically, an autoencoder -- jointly learns a precoder and decoder for data symbol detection. Since quantization prevents end-to-end training, we propose a two-step sequential training policy for this model. With synthetic data, our deep learning-based channel estimation can outperform least squares (LS) channel estimation for unquantized (full-resolution) OFDM at average SNRs up to 14 dB. For data detection, our proposed design achieves lower bit error rate (BER) in fading than unquantized OFDM at average SNRs up to 10 dB.