We recently set a new limit on the electric dipole moment of the electron (eEDM) (J Baron et al and ACME collaboration 2014 Science 343 269–272), which represented an order-of-magnitude improvement on the previous limit and placed more stringent constraints on many charge-parity-violating extensions to the standard model. In this paper we discuss the measurement in detail. The experimental method and associated apparatus are described, together with the techniques used to isolate the eEDM signal. In particular, we detail the way experimental switches were used to suppress effects that can mimic the signal of interest. The methods used to search for systematic errors, and models explaining observed systematic errors, are also described. We briefly discuss possible improvements to the experiment.