The FAST Ultra-Deep Survey (FUDS) is a blind survey that aims for the direct detection of H i in galaxies at redshifts
. The survey uses the multibeam receiver on the Five-hundred-metre Aperture Spherical Telescope (FAST) to map six regions, each of size
at high sensitivity (
) and high-frequency resolution (23 kHz). The survey will enable studies of the evolution of galaxies and their H i content with an eventual sample size of
. We present the science goals, observing strategy, the effects of radio frequency interference at the FAST site, our mitigation strategies and the methods for calibration, data reduction and imaging as applied to initial data. The observations and reductions for the first field, FUDS0, are completed, with around 128 H i galaxies detected in a preliminary analysis. Example spectra are given in this paper, including a comparison with data from the overlapping GAL2577 field of Arecibo Ultra-Deep Survey.