We use the SAURON and GMOS integral field spectrographs to observe the active galactic nucleus (AGN) powered outflow in NGC 1266. This unusual galaxy is relatively nearby (D=30 Mpc), allowing us to investigate the process of AGN feedback in action. We present maps of the kinematics and line strengths of the ionised gas emission lines Halpha, Hbeta, [OIII], [OI], [NII] and [SII], and report on the detection of Sodium D absorption. We use these tracers to explore the structure of the source, derive the ionised and atomic gas kinematics and investigate the gas excitation and physical conditions. NGC 1266 contains two ionised gas components along most lines of sight, tracing the ongoing outflow and a component closer to the galaxy systemic, the origin of which is unclear. This gas appears to be disturbed by a nascent AGN jet. We confirm that the outflow in NGC 1266 is truly multiphase, containing radio plasma, atomic, molecular and ionised gas and X-ray emitting plasma. The outflow has velocities up to \pm900 km/s away from the systemic velocity, and is very likely to be removing significant amounts of cold gas from the galaxy. The LINER-like line-emission in NGC 1266 is extended, and likely arises from fast shocks caused by the interaction of the radio jet with the ISM. These shocks have velocities of up to 800 km/s, which match well with the observed velocity of the outflow. Sodium D equivalent width profiles are used to set constraints on the size and orientation of the outflow. The ionised gas morphology correlates with the nascent radio jets observed in 1.4 GHz and 5 GHz continuum emission, supporting the suggestion that an AGN jet is providing the energy required to drive the outflow.