  We recently reported a new measurement of the electron's electric dipole
moment using YbF molecules [Nature 473, 493 (2011)]. Here, we give a more
detailed description of the methods used to make this measurement, along with a
fuller analysis of the data. We show how our methods isolate the electric
dipole moment from imperfections in the experiment that might mimic it. We
describe the systematic errors that we discovered, and the small corrections
that we made to account for these. By making a set of additional measurements
with greatly exaggerated experimental imperfections, we find upper bounds on
possible uncorrected systematic errors which we use to determine the systematic
uncertainty in the measurement. We also calculate the size of some systematic
effects that have been important in previous electric dipole moment
measurements, such as the motional magnetic field effect and the geometric
phase, and show them to be negligibly small in the present experiment. Our
result is consistent with an electric dipole moment of zero, so we provide
upper bounds to its size at various confidence levels. Finally, we review the
prospects for future improvements in the precision of the experiment.
