Zero-field nuclear magnetic resonance (NMR) spectroscopy is emerging as a new, potentially portable, and cost-effective NMR modality with the ability to provide information-rich, high-resolution spectra. We present simple rules for analysis of zero-field NMR spectra based on first-order perturbation theory and the addition of angular momenta. These rules allow for the prediction of observed spectral lines without numerical simulation. Results are presented for a few small organic molecules with characteristic spin topologies, demonstrating unambiguous assignment of peaks, highlighting the potential of zero-field NMR as a tool for chemical identification.