The Next Generation Transit Survey (NGTS) is an ongoing wide-field exoplanet transit survey at ESO Paranal Observatory, Chile. It is searching for Neptune and super-Earth size planets around nearby stars using 12 robotic telescopes covering a total field of view of 88.8 sq. deg. on the sky. The instruments are optimised for sensitivity to stars of spectral type K and early-M, and the experiment will provide prime targets for further characterisation with current and future instruments. We have analysed NGTS photometry from 30 fields observed during its first year in operation to assess the achieved photometric precision. We build a white noise model to estimate the level of systematic (red) noise in the photometry, and find a median red noise level of 0.82±0.10 mmag in our fields over their full observing season. We develop an automated way of detecting variable stars using our noise model, and find 1245 (1.31%) variable stars at high confidence. Their periods are found with an implementation of the generalised Lomb-Scargle periodogram, and we find a 71% matching rate with known variables in our fields from variable star catalogues. Excluding known variables, we discover ∼900 new variable stars that include rapid pulsators (δ Scuti, RR Lyrae), short-period eclipsing binaries, Cepheids, and semiregular variables. We also find an overdensity of variables at periods of 10–30 days at amplitudes of less than 1%, which we find is consistent with main sequence rotation periods for our target stars. If confirmed in future studies, this would be the first time a wide-field survey has been able to detect these signals, opening up new studies on stellar evolution of low-mass stars from the ground.